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diagramy a indexy způsobilosti",{"type":1096,"value":1097,"toc":6700},"minimark",[1098,1102,1436,1441,1451,1458,1513,1524,1534,1537,1562,1566,1572,1592,1595,1602,1608,1619,1622,1651,1655,1658,1726,1817,1847,1892,2018,2021,2141,2236,2487,2530,2680,2909,3125,3244,3251,3260,3364,3371,3399,3468,3537,3577,3609,3747,3839,3897,3901,3904,3993,4009,4085,4129,4274,4282,4362,4369,4385,4442,4449,4524,4542,4575,4591,4658,4674,4714,4719,4791,4795,4837,4858,4877,4923,4974,4977,5169,5194,5197,5278,5365,5413,5504,5626,5630,5764,5804,5811,5818,5822,5889,6020,6090,6375,6379,6604,6608,6664,6667,6675,6682,6689,6696],[1099,1100,1094],"h1",{"id":1101},"regulační-diagramy-a-indexy-způsobilosti",[1103,1104,1109,1123],"aside",{"className":1105,"dataCallout":1108},[1106,1107],"callout","callout-default","tldr",[1110,1111,1114,1122],"p",{"className":1112},[1113],"callout-title",[1115,1116],"span",{"className":1117,"ariaHidden":1121},[1118,1119,1120],"iconify","i-lucide:info","callout-icon","true","V 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",[1115,1178,1180],{"className":1179},[1136],[1138,1181,1182],{"xmlns":1140},[1142,1183,1184,1201],{},[1145,1185,1186,1188,1194,1196,1199],{},[1148,1187,1151],{"stretchy":1150},[1153,1189,1190,1192],{"accent":1121},[1156,1191,1158],{},[1148,1193,1161],{},[1148,1195,1164],{"separator":1121},[1156,1197,1198],{},"s",[1148,1200,1170],{"stretchy":1150},[1172,1202,1203],{"encoding":1174},"(\\bar{x}, s)"," a ",[1115,1206,1208],{"className":1207},[1136],[1138,1209,1210],{"xmlns":1140},[1142,1211,1212,1244],{},[1145,1213,1214,1216,1224,1226,1242],{},[1148,1215,1151],{"stretchy":1150},[1217,1218,1219,1221],"msub",{},[1156,1220,1158],{},[1156,1222,1223],{},"i",[1148,1225,1164],{"separator":1121},[1217,1227,1228,1230],{},[1156,1229,1167],{},[1145,1231,1232,1235,1238,1240],{},[1156,1233,1234],{},"k",[1156,1236,1237],{},"l",[1148,1239,1164],{"separator":1121},[1156,1241,1223],{},[1148,1243,1170],{"stretchy":1150},[1172,1245,1246],{"encoding":1174},"(x_i, R_{kl,i})",".",[1127,1249,1250,1251,1265,1266,1280,1281,1298,1299,1312],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,1252,1254],{"className":1253},[1136],[1138,1255,1256],{"xmlns":1140},[1142,1257,1258,1263],{},[1145,1259,1260],{},[1156,1261,1262],{},"c",[1172,1264,1262],{"encoding":1174}," (konstantní rozsah) a ",[1115,1267,1269],{"className":1268},[1136],[1138,1270,1271],{"xmlns":1140},[1142,1272,1273,1278],{},[1145,1274,1275],{},[1156,1276,1277],{},"u",[1172,1279,1277],{"encoding":1174}," (nekonstantní rozsah), počet neshodných produktů ",[1115,1282,1284],{"className":1283},[1136],[1138,1285,1286],{"xmlns":1140},[1142,1287,1288,1295],{},[1145,1289,1290,1293],{},[1156,1291,1292],{},"n",[1156,1294,1110],{},[1172,1296,1297],{"encoding":1174},"np"," (konstantní rozsah) a jejich podíl ",[1115,1300,1302],{"className":1301},[1136],[1138,1303,1304],{"xmlns":1140},[1142,1305,1306,1310],{},[1145,1307,1308],{},[1156,1309,1110],{},[1172,1311,1110],{"encoding":1174}," (nekonstantní rozsah).",[1127,1314,1315],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1127,1317,1318,1319,1176,1338,1176,1360,1176,1383,1407,1408,1429],{},"Indexy způsobilosti ",[1115,1320,1322],{"className":1321},[1136],[1138,1323,1324],{"xmlns":1140},[1142,1325,1326,1335],{},[1145,1327,1328],{},[1217,1329,1330,1333],{},[1156,1331,1332],{},"C",[1156,1334,1110],{},[1172,1336,1337],{"encoding":1174},"C_p",[1115,1339,1341],{"className":1340},[1136],[1138,1342,1343],{"xmlns":1140},[1142,1344,1345,1357],{},[1145,1346,1347],{},[1217,1348,1349,1351],{},[1156,1350,1332],{},[1145,1352,1353,1355],{},[1156,1354,1110],{},[1156,1356,1234],{},[1172,1358,1359],{"encoding":1174},"C_{pk}",[1115,1361,1363],{"className":1362},[1136],[1138,1364,1365],{"xmlns":1140},[1142,1366,1367,1380],{},[1145,1368,1369],{},[1217,1370,1371,1373],{},[1156,1372,1332],{},[1145,1374,1375,1377],{},[1156,1376,1110],{},[1156,1378,1379],{},"m",[1172,1381,1382],{"encoding":1174},"C_{pm}",[1115,1384,1386],{"className":1385},[1136],[1138,1387,1388],{"xmlns":1140},[1142,1389,1390,1404],{},[1145,1391,1392],{},[1217,1393,1394,1396],{},[1156,1395,1332],{},[1145,1397,1398,1400,1402],{},[1156,1399,1110],{},[1156,1401,1379],{},[1156,1403,1234],{},[1172,1405,1406],{"encoding":1174},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,1409,1411],{"className":1410},[1136],[1138,1412,1413],{"xmlns":1140},[1142,1414,1415,1427],{},[1145,1416,1417],{},[1217,1418,1419,1421],{},[1156,1420,1332],{},[1145,1422,1423,1425],{},[1156,1424,1110],{},[1156,1426,1234],{},[1172,1428,1359],{"encoding":1174}," navíc zohledňuje vychýlení střední hodnoty.",[1127,1431,1432,1433,1247],{},"V R diagramy i indexy počítá balíček ",[1434,1435,360],"code",{},[1437,1438,1440],"h2",{"id":1439},"statistická-regulace-procesu","Statistická regulace procesu",[1110,1442,1443,1444,1447,1448,1247],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1445,1446,1440],"strong",{}," je preventivní nástroj řízení jakosti: analyzuje chování výrobního procesu, umožňuje včas odhalit odchylky od normy a zasáhnout tak, aby proces zůstal dlouhodobě na požadované a stabilní úrovni — ve ",[1445,1449,1450],{},"statisticky zvládnutém stavu",[1110,1452,1453,1454,1457],{},"Teorie regulace vychází z ",[1445,1455,1456],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1459,1460,1461,1476],"table",{},[1462,1463,1464],"thead",{},[1465,1466,1467,1470,1473],"tr",{},[1468,1469],"th",{},[1468,1471,1472],{},"Náhodné příčiny",[1468,1474,1475],{},"Vymezitelné příčiny",[1477,1478,1479,1491,1502],"tbody",{},[1465,1480,1481,1485,1488],{},[1482,1483,1484],"td",{},"Povaha",[1482,1486,1487],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1482,1489,1490],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1465,1492,1493,1496,1499],{},[1482,1494,1495],{},"Stav procesu",[1482,1497,1498],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1482,1500,1501],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1465,1503,1504,1507,1510],{},[1482,1505,1506],{},"Příklady",[1482,1508,1509],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1482,1511,1512],{},"změna materiálu, nezaškolená obsluha",[1110,1514,1515,1516,1519,1520,1523],{},"Vymezitelné příčiny jsou ",[1445,1517,1518],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1445,1521,1522],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,1525,1526],{},[1527,1528],"img",{"alt":1529,"className":1530,"src":1533},"mask-ilu-pricin-variability",[1531,1532],"wikilink","wikilink-broken","\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,1535,1536],{},"Regulace probíhá ve třech fázích:",[1538,1539,1540,1550,1556],"ol",{},[1127,1541,1542,1545,1546,1549],{},[1445,1543,1544],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1445,1547,1548],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1127,1551,1552,1555],{},[1445,1553,1554],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1127,1557,1558,1561],{},[1445,1559,1560],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1437,1563,1565],{"id":1564},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,1567,1568,1571],{},[1445,1569,1570],{},"Regulační diagram"," je grafický prostředek pro zobrazení vývoje variability procesu v čase. Popisuje statistickou zvládnutelnost procesu a dává signál, že na proces začala působit vymezitelná příčina; na jeho základě se do procesu zasáhne s cílem příčinu odstranit.",[1124,1573,1574,1580,1586],{},[1127,1575,1576,1579],{},[1445,1577,1578],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1127,1581,1582,1585],{},[1445,1583,1584],{},"UCL"," — horní akční regulační mez,",[1127,1587,1588,1591],{},[1445,1589,1590],{},"LCL"," — dolní akční regulační mez.",[1110,1593,1594],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,1596,1597],{},[1527,1598],{"alt":1599,"className":1600,"src":1601},"mask-rd-schema",[1531,1532],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,1603,1604,1607],{},[1445,1605,1606],{},"Interpretace:"," jsou-li všechny body uvnitř akčních mezí, je proces statisticky zvládnutý (nepůsobí žádná vymezitelná příčina). Je-li některý bod mimo meze, lze usuzovat, že proces není ve statisticky zvládnutém stavu; je třeba identifikovat vymezitelnou příčinu a přijmout opatření k jejímu odstranění.",[1110,1609,1610,1611,1614,1615,1618],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1445,1612,1613],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1445,1616,1617],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,1620,1621],{},"Postup při konstrukci regulačního diagramu:",[1538,1623,1624,1627,1630,1633,1636,1639,1642,1645,1648],{},[1127,1625,1626],{},"volba regulované veličiny,",[1127,1628,1629],{},"sběr a záznam dat,",[1127,1631,1632],{},"ověření požadovaných předpokladů o datech,",[1127,1634,1635],{},"volba rozsahu logických podskupin,",[1127,1637,1638],{},"volba vhodného regulačního diagramu,",[1127,1640,1641],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1127,1643,1644],{},"ověření a zajištění statistické zvládnutosti procesu,",[1127,1646,1647],{},"ověření způsobilosti procesu,",[1127,1649,1650],{},"vlastní regulace procesu.",[1437,1652,1654],{"id":1653},"regulace-měřením","Regulace měřením",[1110,1656,1657],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1124,1659,1660,1663],{},[1127,1661,1662],{},"jednotlivá měření byla vzájemně nezávislá,",[1127,1664,1665,1666,1681,1682,1697,1698,1711,1712,1725],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,1667,1669],{"className":1668},[1136],[1138,1670,1671],{"xmlns":1140},[1142,1672,1673,1678],{},[1145,1674,1675],{},[1156,1676,1677],{},"μ",[1172,1679,1680],{"encoding":1174},"\\mu"," a směrodatnou odchylkou ",[1115,1683,1685],{"className":1684},[1136],[1138,1686,1687],{"xmlns":1140},[1142,1688,1689,1694],{},[1145,1690,1691],{},[1156,1692,1693],{},"σ",[1172,1695,1696],{"encoding":1174},"\\sigma"," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,1699,1701],{"className":1700},[1136],[1138,1702,1703],{"xmlns":1140},[1142,1704,1705,1709],{},[1145,1706,1707],{},[1156,1708,1677],{},[1172,1710,1680],{"encoding":1174}," je hodnota, na niž je proces nastaven, ",[1115,1713,1715],{"className":1714},[1136],[1138,1716,1717],{"xmlns":1140},[1142,1718,1719,1723],{},[1145,1720,1721],{},[1156,1722,1693],{},[1172,1724,1696],{"encoding":1174}," charakterizuje jeho přesnost.",[1110,1727,1728,1729,1176,1754,1204,1779,1816],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,1730,1732],{"className":1731},[1136],[1138,1733,1734],{"xmlns":1140},[1142,1735,1736,1752],{},[1145,1737,1738,1740,1746,1748,1750],{},[1148,1739,1151],{"stretchy":1150},[1153,1741,1742,1744],{"accent":1121},[1156,1743,1158],{},[1148,1745,1161],{},[1148,1747,1164],{"separator":1121},[1156,1749,1167],{},[1148,1751,1170],{"stretchy":1150},[1172,1753,1175],{"encoding":1174},[1115,1755,1757],{"className":1756},[1136],[1138,1758,1759],{"xmlns":1140},[1142,1760,1761,1777],{},[1145,1762,1763,1765,1771,1773,1775],{},[1148,1764,1151],{"stretchy":1150},[1153,1766,1767,1769],{"accent":1121},[1156,1768,1158],{},[1148,1770,1161],{},[1148,1772,1164],{"separator":1121},[1156,1774,1198],{},[1148,1776,1170],{"stretchy":1150},[1172,1778,1203],{"encoding":1174},[1115,1780,1782],{"className":1781},[1136],[1138,1783,1784],{"xmlns":1140},[1142,1785,1786,1814],{},[1145,1787,1788,1790,1796,1798,1812],{},[1148,1789,1151],{"stretchy":1150},[1217,1791,1792,1794],{},[1156,1793,1158],{},[1156,1795,1223],{},[1148,1797,1164],{"separator":1121},[1217,1799,1800,1802],{},[1156,1801,1167],{},[1145,1803,1804,1806,1808,1810],{},[1156,1805,1234],{},[1156,1807,1237],{},[1148,1809,1164],{"separator":1121},[1156,1811,1223],{},[1148,1813,1170],{"stretchy":1150},[1172,1815,1246],{"encoding":1174},". Výsledkem jsou vždy dva diagramy.",[1818,1819,1821,1822],"h3",{"id":1820},"diagram-xˉrbarx-r","Diagram ",[1115,1823,1825],{"className":1824},[1136],[1138,1826,1827],{"xmlns":1140},[1142,1828,1829,1845],{},[1145,1830,1831,1833,1839,1841,1843],{},[1148,1832,1151],{"stretchy":1150},[1153,1834,1835,1837],{"accent":1121},[1156,1836,1158],{},[1148,1838,1161],{},[1148,1840,1164],{"separator":1121},[1156,1842,1167],{},[1148,1844,1170],{"stretchy":1150},[1172,1846,1175],{"encoding":1174},[1110,1848,1849,1850,1872,1873,1891],{},"Regulované veličiny jsou výběrové průměry ",[1115,1851,1853],{"className":1852},[1136],[1138,1854,1855],{"xmlns":1140},[1142,1856,1857,1869],{},[1145,1858,1859],{},[1217,1860,1861,1867],{},[1153,1862,1863,1865],{"accent":1121},[1156,1864,1158],{},[1148,1866,1161],{},[1156,1868,1223],{},[1172,1870,1871],{"encoding":1174},"\\bar{x}_i"," a výběrová rozpětí ",[1115,1874,1876],{"className":1875},[1136],[1138,1877,1878],{"xmlns":1140},[1142,1879,1880,1888],{},[1145,1881,1882],{},[1217,1883,1884,1886],{},[1156,1885,1167],{},[1156,1887,1223],{},[1172,1889,1890],{"encoding":1174},"R_i"," v logických podskupinách:",[1115,1893,1895],{"className":1894},[1136],[1138,1896,1898],{"xmlns":1140,"display":1897},"block",[1142,1899,1900,2015],{},[1145,1901,1902,1912,1915,1924,1941,1951,1953,1957,1963,1965,1978,1988,1991,2002,2012],{},[1217,1903,1904,1910],{},[1153,1905,1906,1908],{"accent":1121},[1156,1907,1158],{},[1148,1909,1161],{},[1156,1911,1223],{},[1148,1913,1914],{},"=",[1916,1917,1918,1922],"mfrac",{},[1919,1920,1921],"mn",{},"1",[1156,1923,1292],{},[1925,1926,1927,1930,1939],"munderover",{},[1148,1928,1929],{},"∑",[1145,1931,1932,1935,1937],{},[1156,1933,1934],{},"j",[1148,1936,1914],{},[1919,1938,1921],{},[1156,1940,1292],{},[1217,1942,1943,1945],{},[1156,1944,1158],{},[1145,1946,1947,1949],{},[1156,1948,1223],{},[1156,1950,1934],{},[1148,1952,1164],{"separator":1121},[1954,1955],"mspace",{"width":1956},"2em",[1217,1958,1959,1961],{},[1156,1960,1167],{},[1156,1962,1223],{},[1148,1964,1914],{},[1966,1967,1968,1976],"munder",{},[1145,1969,1970,1973],{},[1156,1971,1972],{},"max",[1148,1974,1975],{},"⁡",[1156,1977,1934],{},[1217,1979,1980,1982],{},[1156,1981,1158],{},[1145,1983,1984,1986],{},[1156,1985,1223],{},[1156,1987,1934],{},[1148,1989,1990],{},"−",[1966,1992,1993,2000],{},[1145,1994,1995,1998],{},[1156,1996,1997],{},"min",[1148,1999,1975],{},[1156,2001,1934],{},[1217,2003,2004,2006],{},[1156,2005,1158],{},[1145,2007,2008,2010],{},[1156,2009,1223],{},[1156,2011,1934],{},[1156,2013,1247],{"mathvariant":2014},"normal",[1172,2016,2017],{"encoding":1174},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,2019,2020],{},"Podmínky použití: regulovaná veličina je měřitelná a má normální rozdělení, jednotlivá měření jsou nezávislá, každá logická podskupina má stejný rozsah aspoň dvou měření. Má-li každá podskupina aspoň 4 měření, lze diagram pro výběrový průměr použít i pro data, která nepocházejí z normálního rozdělení.",[1110,2022,2023,2024,2051,2052,2065,2066,1204,2087,2104,2105,2118,2119,2137,2138,1247],{},"Data se zapisují do tabulky: řádek ",[1115,2025,2027],{"className":2026},[1136],[1138,2028,2029],{"xmlns":1140},[1142,2030,2031,2048],{},[1145,2032,2033,2035,2037,2039,2041,2044,2046],{},[1156,2034,1223],{},[1148,2036,1914],{},[1919,2038,1921],{},[1148,2040,1164],{"separator":1121},[1148,2042,2043],{},"…",[1148,2045,1164],{"separator":1121},[1156,2047,1234],{},[1172,2049,2050],{"encoding":1174},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,2053,2055],{"className":2054},[1136],[1138,2056,2057],{"xmlns":1140},[1142,2058,2059,2063],{},[1145,2060,2061],{},[1156,2062,1292],{},[1172,2064,1292],{"encoding":1174}," naměřených hodnot a poslední dva sloupce ",[1115,2067,2069],{"className":2068},[1136],[1138,2070,2071],{"xmlns":1140},[1142,2072,2073,2085],{},[1145,2074,2075],{},[1217,2076,2077,2083],{},[1153,2078,2079,2081],{"accent":1121},[1156,2080,1158],{},[1148,2082,1161],{},[1156,2084,1223],{},[1172,2086,1871],{"encoding":1174},[1115,2088,2090],{"className":2089},[1136],[1138,2091,2092],{"xmlns":1140},[1142,2093,2094,2102],{},[1145,2095,2096],{},[1217,2097,2098,2100],{},[1156,2099,1167],{},[1156,2101,1223],{},[1172,2103,1890],{"encoding":1174},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,2106,2108],{"className":2107},[1136],[1138,2109,2110],{"xmlns":1140},[1142,2111,2112,2116],{},[1145,2113,2114],{},[1156,2115,1167],{},[1172,2117,1167],{"encoding":1174},", potom diagram ",[1115,2120,2122],{"className":2121},[1136],[1138,2123,2124],{"xmlns":1140},[1142,2125,2126,2134],{},[1145,2127,2128],{},[1153,2129,2130,2132],{"accent":1121},[1156,2131,1158],{},[1148,2133,1161],{},[1172,2135,2136],{"encoding":1174},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[1434,2139,2140],{},"qcc()",[1103,2142,2146,2154],{"className":2143,"dataCallout":2145},[1106,2144],"callout-example","example",[1110,2147,2149,2153],{"className":2148},[1113],[1115,2150],{"className":2151,"ariaHidden":1121},[1118,2152,1120],"i-lucide:flask-conical","Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,2155,2156,2157,2171,2172,1176,2191,2210,2211,1247],{},"Naměřená data znaku jakosti ",[1115,2158,2160],{"className":2159},[1136],[1138,2161,2162],{"xmlns":1140},[1142,2163,2164,2169],{},[1145,2165,2166],{},[1156,2167,2168],{},"X",[1172,2170,2168],{"encoding":1174}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,2173,2175],{"className":2174},[1136],[1138,2176,2177],{"xmlns":1140},[1142,2178,2179,2188],{},[1145,2180,2181,2183,2185],{},[1156,2182,1234],{},[1148,2184,1914],{},[1919,2186,2187],{},"20",[1172,2189,2190],{"encoding":1174},"k=20",[1115,2192,2194],{"className":2193},[1136],[1138,2195,2196],{"xmlns":1140},[1142,2197,2198,2207],{},[1145,2199,2200,2202,2204],{},[1156,2201,1292],{},[1148,2203,1914],{},[1919,2205,2206],{},"4",[1172,2208,2209],{"encoding":1174},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,2212,2214],{"className":2213},[1136],[1138,2215,2216],{"xmlns":1140},[1142,2217,2218,2234],{},[1145,2219,2220,2222,2228,2230,2232],{},[1148,2221,1151],{"stretchy":1150},[1153,2223,2224,2226],{"accent":1121},[1156,2225,1158],{},[1148,2227,1161],{},[1148,2229,1164],{"separator":1121},[1156,2231,1167],{},[1148,2233,1170],{"stretchy":1150},[1172,2235,1175],{"encoding":1174},[1459,2237,2238,2355],{},[1462,2239,2240],{},[1465,2241,2242,2257,2281,2306,2331],{},[1468,2243,2244],{},[1115,2245,2247],{"className":2246},[1136],[1138,2248,2249],{"xmlns":1140},[1142,2250,2251,2255],{},[1145,2252,2253],{},[1156,2254,1223],{},[1172,2256,1223],{"encoding":1174},[1468,2258,2259],{},[1115,2260,2262],{"className":2261},[1136],[1138,2263,2264],{"xmlns":1140},[1142,2265,2266,2278],{},[1145,2267,2268],{},[1217,2269,2270,2272],{},[1156,2271,1158],{},[1145,2273,2274,2276],{},[1156,2275,1223],{},[1919,2277,1921],{},[1172,2279,2280],{"encoding":1174},"x_{i1}",[1468,2282,2283],{},[1115,2284,2286],{"className":2285},[1136],[1138,2287,2288],{"xmlns":1140},[1142,2289,2290,2303],{},[1145,2291,2292],{},[1217,2293,2294,2296],{},[1156,2295,1158],{},[1145,2297,2298,2300],{},[1156,2299,1223],{},[1919,2301,2302],{},"2",[1172,2304,2305],{"encoding":1174},"x_{i2}",[1468,2307,2308],{},[1115,2309,2311],{"className":2310},[1136],[1138,2312,2313],{"xmlns":1140},[1142,2314,2315,2328],{},[1145,2316,2317],{},[1217,2318,2319,2321],{},[1156,2320,1158],{},[1145,2322,2323,2325],{},[1156,2324,1223],{},[1919,2326,2327],{},"3",[1172,2329,2330],{"encoding":1174},"x_{i3}",[1468,2332,2333],{},[1115,2334,2336],{"className":2335},[1136],[1138,2337,2338],{"xmlns":1140},[1142,2339,2340,2352],{},[1145,2341,2342],{},[1217,2343,2344,2346],{},[1156,2345,1158],{},[1145,2347,2348,2350],{},[1156,2349,1223],{},[1919,2351,2206],{},[1172,2353,2354],{"encoding":1174},"x_{i4}",[1477,2356,2357,2372,2388,2404,2420,2433,2448,2460,2475],{},[1465,2358,2359,2361,2364,2367,2370],{},[1482,2360,1921],{},[1482,2362,2363],{},"106",[1482,2365,2366],{},"98",[1482,2368,2369],{},"101",[1482,2371,2369],{},[1465,2373,2374,2376,2379,2382,2385],{},[1482,2375,2302],{},[1482,2377,2378],{},"95",[1482,2380,2381],{},"94",[1482,2383,2384],{},"108",[1482,2386,2387],{},"92",[1465,2389,2390,2392,2395,2398,2401],{},[1482,2391,2327],{},[1482,2393,2394],{},"122",[1482,2396,2397],{},"105",[1482,2399,2400],{},"103",[1482,2402,2403],{},"133",[1465,2405,2406,2408,2411,2414,2417],{},[1482,2407,2206],{},[1482,2409,2410],{},"113",[1482,2412,2413],{},"71",[1482,2415,2416],{},"128",[1482,2418,2419],{},"135",[1465,2421,2422,2425,2427,2429,2431],{},[1482,2423,2424],{},"5",[1482,2426,2369],{},[1482,2428,2387],{},[1482,2430,2400],{},[1482,2432,2387],{},[1465,2434,2435,2438,2440,2442,2445],{},[1482,2436,2437],{},"6",[1482,2439,2366],{},[1482,2441,2400],{},[1482,2443,2444],{},"97",[1482,2446,2447],{},"99",[1465,2449,2450,2452,2454,2456,2458],{},[1482,2451,2043],{},[1482,2453,2043],{},[1482,2455,2043],{},[1482,2457,2043],{},[1482,2459,2043],{},[1465,2461,2462,2465,2467,2469,2472],{},[1482,2463,2464],{},"19",[1482,2466,2416],{},[1482,2468,2403],{},[1482,2470,2471],{},"120",[1482,2473,2474],{},"125",[1465,2476,2477,2479,2481,2483,2485],{},[1482,2478,2187],{},[1482,2480,2366],{},[1482,2482,2400],{},[1482,2484,2444],{},[1482,2486,2447],{},[1110,2488,2489,2490,2511,2512,2529],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,2491,2493],{"className":2492},[1136],[1138,2494,2495],{"xmlns":1140},[1142,2496,2497,2509],{},[1145,2498,2499],{},[1217,2500,2501,2507],{},[1153,2502,2503,2505],{"accent":1121},[1156,2504,1158],{},[1148,2506,1161],{},[1156,2508,1223],{},[1172,2510,1871],{"encoding":1174}," a rozpětí ",[1115,2513,2515],{"className":2514},[1136],[1138,2516,2517],{"xmlns":1140},[1142,2518,2519,2527],{},[1145,2520,2521],{},[1217,2522,2523,2525],{},[1156,2524,1167],{},[1156,2526,1223],{},[1172,2528,1890],{"encoding":1174},":",[1459,2531,2532,2593],{},[1462,2533,2534],{},[1465,2535,2536,2551,2574],{},[1468,2537,2538],{},[1115,2539,2541],{"className":2540},[1136],[1138,2542,2543],{"xmlns":1140},[1142,2544,2545,2549],{},[1145,2546,2547],{},[1156,2548,1223],{},[1172,2550,1223],{"encoding":1174},[1468,2552,2553],{},[1115,2554,2556],{"className":2555},[1136],[1138,2557,2558],{"xmlns":1140},[1142,2559,2560,2572],{},[1145,2561,2562],{},[1217,2563,2564,2570],{},[1153,2565,2566,2568],{"accent":1121},[1156,2567,1158],{},[1148,2569,1161],{},[1156,2571,1223],{},[1172,2573,1871],{"encoding":1174},[1468,2575,2576],{},[1115,2577,2579],{"className":2578},[1136],[1138,2580,2581],{"xmlns":1140},[1142,2582,2583,2591],{},[1145,2584,2585],{},[1217,2586,2587,2589],{},[1156,2588,1167],{},[1156,2590,1223],{},[1172,2592,1890],{"encoding":1174},[1477,2594,2595,2605,2615,2625,2635,2645,2654,2662,2672],{},[1465,2596,2597,2599,2602],{},[1482,2598,1921],{},[1482,2600,2601],{},"101,50",[1482,2603,2604],{},"8",[1465,2606,2607,2609,2612],{},[1482,2608,2302],{},[1482,2610,2611],{},"97,25",[1482,2613,2614],{},"16",[1465,2616,2617,2619,2622],{},[1482,2618,2327],{},[1482,2620,2621],{},"115,75",[1482,2623,2624],{},"30",[1465,2626,2627,2629,2632],{},[1482,2628,2206],{},[1482,2630,2631],{},"111,75",[1482,2633,2634],{},"64",[1465,2636,2637,2639,2642],{},[1482,2638,2424],{},[1482,2640,2641],{},"97,00",[1482,2643,2644],{},"11",[1465,2646,2647,2649,2652],{},[1482,2648,2437],{},[1482,2650,2651],{},"99,25",[1482,2653,2437],{},[1465,2655,2656,2658,2660],{},[1482,2657,2043],{},[1482,2659,2043],{},[1482,2661,2043],{},[1465,2663,2664,2666,2669],{},[1482,2665,2464],{},[1482,2667,2668],{},"126,50",[1482,2670,2671],{},"13",[1465,2673,2674,2676,2678],{},[1482,2675,2187],{},[1482,2677,2651],{},[1482,2679,2437],{},[1110,2681,2682,2683,2696,2697,1176,2725,1176,2755,2784,2785,2807,2808,1176,2835,1176,2864,2891,2892,1247],{},"Nejprve se posoudí diagram ",[1115,2684,2686],{"className":2685},[1136],[1138,2687,2688],{"xmlns":1140},[1142,2689,2690,2694],{},[1145,2691,2692],{},[1156,2693,1167],{},[1172,2695,1167],{"encoding":1174}," na všech 20 podskupinách: ",[1115,2698,2700],{"className":2699},[1136],[1138,2701,2702],{"xmlns":1140},[1142,2703,2704,2722],{},[1145,2705,2706,2708,2711,2713,2715,2717,2719],{},[1156,2707,1332],{},[1156,2709,2710],{},"L",[1148,2712,1151],{"stretchy":1150},[1156,2714,1167],{},[1148,2716,1170],{"stretchy":1150},[1148,2718,1914],{},[1919,2720,2721],{},"15,8",[1172,2723,2724],{"encoding":1174},"CL(R)=15{,}8",[1115,2726,2728],{"className":2727},[1136],[1138,2729,2730],{"xmlns":1140},[1142,2731,2732,2752],{},[1145,2733,2734,2737,2739,2741,2743,2745,2747,2749],{},[1156,2735,2736],{},"U",[1156,2738,1332],{},[1156,2740,2710],{},[1148,2742,1151],{"stretchy":1150},[1156,2744,1167],{},[1148,2746,1170],{"stretchy":1150},[1148,2748,1914],{},[1919,2750,2751],{},"36,06",[1172,2753,2754],{"encoding":1174},"UCL(R)=36{,}06",[1115,2756,2758],{"className":2757},[1136],[1138,2759,2760],{"xmlns":1140},[1142,2761,2762,2781],{},[1145,2763,2764,2766,2768,2770,2772,2774,2776,2778],{},[1156,2765,2710],{},[1156,2767,1332],{},[1156,2769,2710],{},[1148,2771,1151],{"stretchy":1150},[1156,2773,1167],{},[1148,2775,1170],{"stretchy":1150},[1148,2777,1914],{},[1919,2779,2780],{},"0",[1172,2782,2783],{"encoding":1174},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,2786,2788],{"className":2787},[1136],[1138,2789,2790],{"xmlns":1140},[1142,2791,2792,2804],{},[1145,2793,2794,2800,2802],{},[1217,2795,2796,2798],{},[1156,2797,1167],{},[1919,2799,2206],{},[1148,2801,1914],{},[1919,2803,2634],{},[1172,2805,2806],{"encoding":1174},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,2809,2811],{"className":2810},[1136],[1138,2812,2813],{"xmlns":1140},[1142,2814,2815,2832],{},[1145,2816,2817,2819,2821,2823,2825,2827,2829],{},[1156,2818,1332],{},[1156,2820,2710],{},[1148,2822,1151],{"stretchy":1150},[1156,2824,1167],{},[1148,2826,1170],{"stretchy":1150},[1148,2828,1914],{},[1919,2830,2831],{},"13,26",[1172,2833,2834],{"encoding":1174},"CL(R)=13{,}26",[1115,2836,2838],{"className":2837},[1136],[1138,2839,2840],{"xmlns":1140},[1142,2841,2842,2861],{},[1145,2843,2844,2846,2848,2850,2852,2854,2856,2858],{},[1156,2845,2736],{},[1156,2847,1332],{},[1156,2849,2710],{},[1148,2851,1151],{"stretchy":1150},[1156,2853,1167],{},[1148,2855,1170],{"stretchy":1150},[1148,2857,1914],{},[1919,2859,2860],{},"30,27",[1172,2862,2863],{"encoding":1174},"UCL(R)=30{,}27",[1115,2865,2867],{"className":2866},[1136],[1138,2868,2869],{"xmlns":1140},[1142,2870,2871,2889],{},[1145,2872,2873,2875,2877,2879,2881,2883,2885,2887],{},[1156,2874,2710],{},[1156,2876,1332],{},[1156,2878,2710],{},[1148,2880,1151],{"stretchy":1150},[1156,2882,1167],{},[1148,2884,1170],{"stretchy":1150},[1148,2886,1914],{},[1919,2888,2780],{},[1172,2890,2783],{"encoding":1174},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,2893,2895],{"className":2894},[1136],[1138,2896,2897],{"xmlns":1140},[1142,2898,2899,2907],{},[1145,2900,2901],{},[1153,2902,2903,2905],{"accent":1121},[1156,2904,1158],{},[1148,2906,1161],{},[1172,2908,2136],{"encoding":1174},[1110,2910,1821,2911,2928,2929,1176,2960,1176,2993,3026,3027,3040,3041,1176,3068,1176,3097,3124],{},[1115,2912,2914],{"className":2913},[1136],[1138,2915,2916],{"xmlns":1140},[1142,2917,2918,2926],{},[1145,2919,2920],{},[1153,2921,2922,2924],{"accent":1121},[1156,2923,1158],{},[1148,2925,1161],{},[1172,2927,2136],{"encoding":1174}," bez čtvrté podskupiny dává ",[1115,2930,2932],{"className":2931},[1136],[1138,2933,2934],{"xmlns":1140},[1142,2935,2936,2957],{},[1145,2937,2938,2940,2942,2944,2950,2952,2954],{},[1156,2939,1332],{},[1156,2941,2710],{},[1148,2943,1151],{"stretchy":1150},[1153,2945,2946,2948],{"accent":1121},[1156,2947,1158],{},[1148,2949,1161],{},[1148,2951,1170],{"stretchy":1150},[1148,2953,1914],{},[1919,2955,2956],{},"102,01",[1172,2958,2959],{"encoding":1174},"CL(\\bar{x})=102{,}01",[1115,2961,2963],{"className":2962},[1136],[1138,2964,2965],{"xmlns":1140},[1142,2966,2967,2990],{},[1145,2968,2969,2971,2973,2975,2977,2983,2985,2987],{},[1156,2970,2736],{},[1156,2972,1332],{},[1156,2974,2710],{},[1148,2976,1151],{"stretchy":1150},[1153,2978,2979,2981],{"accent":1121},[1156,2980,1158],{},[1148,2982,1161],{},[1148,2984,1170],{"stretchy":1150},[1148,2986,1914],{},[1919,2988,2989],{},"111,68",[1172,2991,2992],{"encoding":1174},"UCL(\\bar{x})=111{,}68",[1115,2994,2996],{"className":2995},[1136],[1138,2997,2998],{"xmlns":1140},[1142,2999,3000,3023],{},[1145,3001,3002,3004,3006,3008,3010,3016,3018,3020],{},[1156,3003,2710],{},[1156,3005,1332],{},[1156,3007,2710],{},[1148,3009,1151],{"stretchy":1150},[1153,3011,3012,3014],{"accent":1121},[1156,3013,1158],{},[1148,3015,1161],{},[1148,3017,1170],{"stretchy":1150},[1148,3019,1914],{},[1919,3021,3022],{},"92,34",[1172,3024,3025],{"encoding":1174},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,3028,3030],{"className":3029},[1136],[1138,3031,3032],{"xmlns":1140},[1142,3033,3034,3038],{},[1145,3035,3036],{},[1156,3037,1167],{},[1172,3039,1167],{"encoding":1174}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,3042,3044],{"className":3043},[1136],[1138,3045,3046],{"xmlns":1140},[1142,3047,3048,3065],{},[1145,3049,3050,3052,3054,3056,3058,3060,3062],{},[1156,3051,1332],{},[1156,3053,2710],{},[1148,3055,1151],{"stretchy":1150},[1156,3057,1167],{},[1148,3059,1170],{"stretchy":1150},[1148,3061,1914],{},[1919,3063,3064],{},"12,29",[1172,3066,3067],{"encoding":1174},"CL(R)=12{,}29",[1115,3069,3071],{"className":3070},[1136],[1138,3072,3073],{"xmlns":1140},[1142,3074,3075,3094],{},[1145,3076,3077,3079,3081,3083,3085,3087,3089,3091],{},[1156,3078,2736],{},[1156,3080,1332],{},[1156,3082,2710],{},[1148,3084,1151],{"stretchy":1150},[1156,3086,1167],{},[1148,3088,1170],{"stretchy":1150},[1148,3090,1914],{},[1919,3092,3093],{},"28,06",[1172,3095,3096],{"encoding":1174},"UCL(R)=28{,}06",[1115,3098,3100],{"className":3099},[1136],[1138,3101,3102],{"xmlns":1140},[1142,3103,3104,3122],{},[1145,3105,3106,3108,3110,3112,3114,3116,3118,3120],{},[1156,3107,2710],{},[1156,3109,1332],{},[1156,3111,2710],{},[1148,3113,1151],{"stretchy":1150},[1156,3115,1167],{},[1148,3117,1170],{"stretchy":1150},[1148,3119,1914],{},[1919,3121,2780],{},[1172,3123,2783],{"encoding":1174}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,3126,3127,3128,3145,3146,1176,3177,1176,3210,3243],{},"Konečný diagram ",[1115,3129,3131],{"className":3130},[1136],[1138,3132,3133],{"xmlns":1140},[1142,3134,3135,3143],{},[1145,3136,3137],{},[1153,3138,3139,3141],{"accent":1121},[1156,3140,1158],{},[1148,3142,1161],{},[1172,3144,2136],{"encoding":1174}," na stejných 17 podskupinách má ",[1115,3147,3149],{"className":3148},[1136],[1138,3150,3151],{"xmlns":1140},[1142,3152,3153,3174],{},[1145,3154,3155,3157,3159,3161,3167,3169,3171],{},[1156,3156,1332],{},[1156,3158,2710],{},[1148,3160,1151],{"stretchy":1150},[1153,3162,3163,3165],{"accent":1121},[1156,3164,1158],{},[1148,3166,1161],{},[1148,3168,1170],{"stretchy":1150},[1148,3170,1914],{},[1919,3172,3173],{},"99,76",[1172,3175,3176],{"encoding":1174},"CL(\\bar{x})=99{,}76",[1115,3178,3180],{"className":3179},[1136],[1138,3181,3182],{"xmlns":1140},[1142,3183,3184,3207],{},[1145,3185,3186,3188,3190,3192,3194,3200,3202,3204],{},[1156,3187,2736],{},[1156,3189,1332],{},[1156,3191,2710],{},[1148,3193,1151],{"stretchy":1150},[1153,3195,3196,3198],{"accent":1121},[1156,3197,1158],{},[1148,3199,1161],{},[1148,3201,1170],{"stretchy":1150},[1148,3203,1914],{},[1919,3205,3206],{},"108,73",[1172,3208,3209],{"encoding":1174},"UCL(\\bar{x})=108{,}73",[1115,3211,3213],{"className":3212},[1136],[1138,3214,3215],{"xmlns":1140},[1142,3216,3217,3240],{},[1145,3218,3219,3221,3223,3225,3227,3233,3235,3237],{},[1156,3220,2710],{},[1156,3222,1332],{},[1156,3224,2710],{},[1148,3226,1151],{"stretchy":1150},[1153,3228,3229,3231],{"accent":1121},[1156,3230,1158],{},[1148,3232,1161],{},[1148,3234,1170],{"stretchy":1150},[1148,3236,1914],{},[1919,3238,3239],{},"90,80",[1172,3241,3242],{"encoding":1174},"LCL(\\bar{x})=90{,}80"," — všechny výběrové průměry leží uvnitř mezí, proces je zvládnutý. Protože bylo vyřazeno několik podskupin, je vhodné měření doplnit tak, aby se pracovalo s počtem podskupin mezi 20 a 25.",[1110,3245,3246],{},[1527,3247],{"alt":3248,"className":3249,"src":3250},"mask-rd-priklad1-meze",[1531,1532],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,3252,3253,3254,3256,3257,3259],{},"V R se diagramy sestrojí funkcí ",[1434,3255,2140],{}," z balíčku ",[1434,3258,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3261,3262,3266],"pre",{"className":3263,"code":3264,"language":71,"meta":3265,"style":3265},"language-r shiki shiki-themes github-light github-light github-dark","library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n","",[1434,3267,3268,3284,3316,3341],{"__ignoreMap":3265},[1115,3269,3271,3275,3278,3281],{"class":3270,"line":10},"line",[1115,3272,3274],{"class":3273},"s8jYJ","library",[1115,3276,1151],{"class":3277},"sxrX7",[1115,3279,360],{"class":3280},"sP4rz",[1115,3282,3283],{"class":3277},")\n",[1115,3285,3286,3289,3292,3296,3298,3302,3304,3307,3310,3314],{"class":3270,"line":27},[1115,3287,3288],{"class":3280},"data",[1115,3290,3291],{"class":3273}," \u003C-",[1115,3293,3295],{"class":3294},"snPdu"," read.table",[1115,3297,1151],{"class":3277},[1115,3299,3301],{"class":3300},"sIIMD","\"3_2.txt\"",[1115,3303,1164],{"class":3273},[1115,3305,3306],{"class":3280}," header",[1115,3308,3309],{"class":3273}," =",[1115,3311,3313],{"class":3312},"sBjJW"," TRUE",[1115,3315,3283],{"class":3277},[1115,3317,3318,3320,3322,3324,3326,3329,3331,3334,3337],{"class":3270,"line":148},[1115,3319,360],{"class":3294},[1115,3321,1151],{"class":3277},[1115,3323,3288],{"class":3280},[1115,3325,1164],{"class":3273},[1115,3327,3328],{"class":3280}," type",[1115,3330,3309],{"class":3273},[1115,3332,3333],{"class":3300}," \"R\"",[1115,3335,3336],{"class":3277},")      ",[1115,3338,3340],{"class":3339},"sCsY4","# diagram R\n",[1115,3342,3343,3345,3347,3349,3351,3353,3355,3358,3361],{"class":3270,"line":111},[1115,3344,360],{"class":3294},[1115,3346,1151],{"class":3277},[1115,3348,3288],{"class":3280},[1115,3350,1164],{"class":3273},[1115,3352,3328],{"class":3280},[1115,3354,3309],{"class":3273},[1115,3356,3357],{"class":3300}," \"xbar\"",[1115,3359,3360],{"class":3277},")   ",[1115,3362,3363],{"class":3339},"# diagram x̄\n",[1110,3365,3366,3367,3370],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[1434,3368,3369],{},"data[-4, ]",") a diagram se sestrojí znovu.",[1818,3372,1821,3374],{"id":3373},"diagram-xˉsbarx-s",[1115,3375,3377],{"className":3376},[1136],[1138,3378,3379],{"xmlns":1140},[1142,3380,3381,3397],{},[1145,3382,3383,3385,3391,3393,3395],{},[1148,3384,1151],{"stretchy":1150},[1153,3386,3387,3389],{"accent":1121},[1156,3388,1158],{},[1148,3390,1161],{},[1148,3392,1164],{"separator":1121},[1156,3394,1198],{},[1148,3396,1170],{"stretchy":1150},[1172,3398,1203],{"encoding":1174},[1110,3400,1849,3401,3422,3423,3441,3442,3467],{},[1115,3402,3404],{"className":3403},[1136],[1138,3405,3406],{"xmlns":1140},[1142,3407,3408,3420],{},[1145,3409,3410],{},[1217,3411,3412,3418],{},[1153,3413,3414,3416],{"accent":1121},[1156,3415,1158],{},[1148,3417,1161],{},[1156,3419,1223],{},[1172,3421,1871],{"encoding":1174}," a výběrové směrodatné odchylky ",[1115,3424,3426],{"className":3425},[1136],[1138,3427,3428],{"xmlns":1140},[1142,3429,3430,3438],{},[1145,3431,3432],{},[1217,3433,3434,3436],{},[1156,3435,1198],{},[1156,3437,1223],{},[1172,3439,3440],{"encoding":1174},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,3443,3445],{"className":3444},[1136],[1138,3446,3447],{"xmlns":1140},[1142,3448,3449,3465],{},[1145,3450,3451,3453,3459,3461,3463],{},[1148,3452,1151],{"stretchy":1150},[1153,3454,3455,3457],{"accent":1121},[1156,3456,1158],{},[1148,3458,1161],{},[1148,3460,1164],{"separator":1121},[1156,3462,1167],{},[1148,3464,1170],{"stretchy":1150},[1172,3466,1175],{"encoding":1174},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3261,3469,3471],{"className":3263,"code":3470,"language":71,"meta":3265,"style":3265},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[1434,3472,3473,3495,3517],{"__ignoreMap":3265},[1115,3474,3475,3477,3479,3481,3483,3485,3487,3489,3491,3493],{"class":3270,"line":10},[1115,3476,3288],{"class":3280},[1115,3478,3291],{"class":3273},[1115,3480,3295],{"class":3294},[1115,3482,1151],{"class":3277},[1115,3484,3301],{"class":3300},[1115,3486,1164],{"class":3273},[1115,3488,3306],{"class":3280},[1115,3490,3309],{"class":3273},[1115,3492,3313],{"class":3312},[1115,3494,3283],{"class":3277},[1115,3496,3497,3499,3501,3503,3505,3507,3509,3512,3514],{"class":3270,"line":27},[1115,3498,360],{"class":3294},[1115,3500,1151],{"class":3277},[1115,3502,3288],{"class":3280},[1115,3504,1164],{"class":3273},[1115,3506,3328],{"class":3280},[1115,3508,3309],{"class":3273},[1115,3510,3511],{"class":3300}," \"S\"",[1115,3513,3336],{"class":3277},[1115,3515,3516],{"class":3339},"# diagram s\n",[1115,3518,3519,3521,3523,3525,3527,3529,3531,3533,3535],{"class":3270,"line":148},[1115,3520,360],{"class":3294},[1115,3522,1151],{"class":3277},[1115,3524,3288],{"class":3280},[1115,3526,1164],{"class":3273},[1115,3528,3328],{"class":3280},[1115,3530,3309],{"class":3273},[1115,3532,3357],{"class":3300},[1115,3534,3360],{"class":3277},[1115,3536,3363],{"class":3339},[1818,3538,1821,3540],{"id":3539},"diagram-xirklix_i-r_kli",[1115,3541,3543],{"className":3542},[1136],[1138,3544,3545],{"xmlns":1140},[1142,3546,3547,3575],{},[1145,3548,3549,3551,3557,3559,3573],{},[1148,3550,1151],{"stretchy":1150},[1217,3552,3553,3555],{},[1156,3554,1158],{},[1156,3556,1223],{},[1148,3558,1164],{"separator":1121},[1217,3560,3561,3563],{},[1156,3562,1167],{},[1145,3564,3565,3567,3569,3571],{},[1156,3566,1234],{},[1156,3568,1237],{},[1148,3570,1164],{"separator":1121},[1156,3572,1223],{},[1148,3574,1170],{"stretchy":1150},[1172,3576,1246],{"encoding":1174},[1110,3578,3579,3580,3605,3606,2529],{},"Používá se za stejných podmínek jako ",[1115,3581,3583],{"className":3582},[1136],[1138,3584,3585],{"xmlns":1140},[1142,3586,3587,3603],{},[1145,3588,3589,3591,3597,3599,3601],{},[1148,3590,1151],{"stretchy":1150},[1153,3592,3593,3595],{"accent":1121},[1156,3594,1158],{},[1148,3596,1161],{},[1148,3598,1164],{"separator":1121},[1156,3600,1167],{},[1148,3602,1170],{"stretchy":1150},[1172,3604,1175],{"encoding":1174},", ale v každé logické podskupině se provede jen jedno měření — například proto, že náklady na kontrolu jsou vysoké nebo kontrola trvá dlouho. Charakteristikou rozptylu je pak ",[1445,3607,3608],{},"klouzavé rozpětí",[1115,3610,3612],{"className":3611},[1136],[1138,3613,3614],{"xmlns":1140,"display":1897},[1142,3615,3616,3744],{},[1145,3617,3618,3632,3634,3637,3643,3645,3657,3659,3661,3664,3666,3668,3670,3672,3674,3676,3678,3680,3682,3684,3686,3700,3702,3714,3728,3742],{},[1217,3619,3620,3622],{},[1156,3621,1167],{},[1145,3623,3624,3626,3628,3630],{},[1156,3625,1234],{},[1156,3627,1237],{},[1148,3629,1164],{"separator":1121},[1156,3631,1223],{},[1148,3633,1914],{},[1156,3635,3636],{"mathvariant":2014},"∣",[1217,3638,3639,3641],{},[1156,3640,1158],{},[1156,3642,1223],{},[1148,3644,1990],{},[1217,3646,3647,3649],{},[1156,3648,1158],{},[1145,3650,3651,3653,3655],{},[1156,3652,1223],{},[1148,3654,1990],{},[1919,3656,1921],{},[1156,3658,3636],{"mathvariant":2014},[1148,3660,1164],{"separator":1121},[1954,3662],{"width":3663},"1em",[1156,3665,1223],{},[1148,3667,1914],{},[1919,3669,2302],{},[1148,3671,1164],{"separator":1121},[1919,3673,2327],{},[1148,3675,1164],{"separator":1121},[1148,3677,2043],{},[1148,3679,1164],{"separator":1121},[1156,3681,1234],{},[1148,3683,1164],{"separator":1121},[1954,3685],{"width":1956},[1217,3687,3688,3694],{},[1153,3689,3690,3692],{"accent":1121},[1156,3691,1167],{},[1148,3693,1161],{},[1145,3695,3696,3698],{},[1156,3697,1234],{},[1156,3699,1237],{},[1148,3701,1914],{},[1916,3703,3704,3706],{},[1919,3705,1921],{},[1145,3707,3708,3710,3712],{},[1156,3709,1234],{},[1148,3711,1990],{},[1919,3713,1921],{},[1925,3715,3716,3718,3726],{},[1148,3717,1929],{},[1145,3719,3720,3722,3724],{},[1156,3721,1223],{},[1148,3723,1914],{},[1919,3725,2302],{},[1156,3727,1234],{},[1217,3729,3730,3732],{},[1156,3731,1167],{},[1145,3733,3734,3736,3738,3740],{},[1156,3735,1234],{},[1156,3737,1237],{},[1148,3739,1164],{"separator":1121},[1156,3741,1223],{},[1156,3743,1247],{"mathvariant":2014},[1172,3745,3746],{"encoding":1174},"R_{kl,i} = |x_i - x_{i-1}|, \\quad i = 2, 3, \\dots, k, \\qquad \\bar{R}_{kl} = \\frac{1}{k-1}\\sum_{i=2}^k R_{kl,i}.",[1110,3748,3749,3750,1204,3768,3794,3795,3820,3821,3838],{},"Regulované veličiny jsou hodnoty ",[1115,3751,3753],{"className":3752},[1136],[1138,3754,3755],{"xmlns":1140},[1142,3756,3757,3765],{},[1145,3758,3759],{},[1217,3760,3761,3763],{},[1156,3762,1158],{},[1156,3764,1223],{},[1172,3766,3767],{"encoding":1174},"x_i",[1115,3769,3771],{"className":3770},[1136],[1138,3772,3773],{"xmlns":1140},[1142,3774,3775,3791],{},[1145,3776,3777],{},[1217,3778,3779,3781],{},[1156,3780,1167],{},[1145,3782,3783,3785,3787,3789],{},[1156,3784,1234],{},[1156,3786,1237],{},[1148,3788,1164],{"separator":1121},[1156,3790,1223],{},[1172,3792,3793],{"encoding":1174},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,3796,3798],{"className":3797},[1136],[1138,3799,3800],{"xmlns":1140},[1142,3801,3802,3818],{},[1145,3803,3804],{},[1217,3805,3806,3808],{},[1156,3807,1167],{},[1145,3809,3810,3812,3814,3816],{},[1156,3811,1234],{},[1156,3813,1237],{},[1148,3815,1164],{"separator":1121},[1156,3817,1223],{},[1172,3819,3793],{"encoding":1174},", potom diagramu ",[1115,3822,3824],{"className":3823},[1136],[1138,3825,3826],{"xmlns":1140},[1142,3827,3828,3836],{},[1145,3829,3830],{},[1217,3831,3832,3834],{},[1156,3833,1158],{},[1156,3835,1223],{},[1172,3837,3767],{"encoding":1174},". Data jsou jeden vektor naměřených hodnot:",[3261,3840,3842],{"className":3263,"code":3841,"language":71,"meta":3265,"style":3265},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[1434,3843,3844,3867],{"__ignoreMap":3265},[1115,3845,3846,3848,3850,3852,3854,3857,3859,3861,3863,3865],{"class":3270,"line":10},[1115,3847,3288],{"class":3280},[1115,3849,3291],{"class":3273},[1115,3851,3295],{"class":3294},[1115,3853,1151],{"class":3277},[1115,3855,3856],{"class":3300},"\"3_3.txt\"",[1115,3858,1164],{"class":3273},[1115,3860,3306],{"class":3280},[1115,3862,3309],{"class":3273},[1115,3864,3313],{"class":3312},[1115,3866,3283],{"class":3277},[1115,3868,3869,3871,3873,3875,3878,3880,3883,3886,3888,3890,3892,3895],{"class":3270,"line":27},[1115,3870,360],{"class":3294},[1115,3872,1151],{"class":3277},[1115,3874,3288],{"class":3280},[1115,3876,3877],{"class":3277},"[",[1115,3879,1164],{"class":3273},[1115,3881,3882],{"class":3312}," 1",[1115,3884,3885],{"class":3277},"]",[1115,3887,1164],{"class":3273},[1115,3889,3328],{"class":3280},[1115,3891,3309],{"class":3273},[1115,3893,3894],{"class":3300}," \"xbar.one\"",[1115,3896,3283],{"class":3277},[1437,3898,3900],{"id":3899},"regulace-srovnáváním","Regulace srovnáváním",[1110,3902,3903],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1459,3905,3906,3919],{},[1462,3907,3908],{},[1465,3909,3910,3913,3916],{},[1468,3911,3912],{},"Sleduje se",[1468,3914,3915],{},"Konstantní rozsah podskupin",[1468,3917,3918],{},"Nekonstantní rozsah podskupin",[1477,3920,3921,3956],{},[1465,3922,3923,3926,3941],{},[1482,3924,3925],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1482,3927,3928],{},[1115,3929,3931],{"className":3930},[1136],[1138,3932,3933],{"xmlns":1140},[1142,3934,3935,3939],{},[1145,3936,3937],{},[1156,3938,1262],{},[1172,3940,1262],{"encoding":1174},[1482,3942,3943],{},[1115,3944,3946],{"className":3945},[1136],[1138,3947,3948],{"xmlns":1140},[1142,3949,3950,3954],{},[1145,3951,3952],{},[1156,3953,1277],{},[1172,3955,1277],{"encoding":1174},[1465,3957,3958,3961,3978],{},[1482,3959,3960],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1482,3962,3963],{},[1115,3964,3966],{"className":3965},[1136],[1138,3967,3968],{"xmlns":1140},[1142,3969,3970,3976],{},[1145,3971,3972,3974],{},[1156,3973,1292],{},[1156,3975,1110],{},[1172,3977,1297],{"encoding":1174},[1482,3979,3980],{},[1115,3981,3983],{"className":3982},[1136],[1138,3984,3985],{"xmlns":1140},[1142,3986,3987,3991],{},[1145,3988,3989],{},[1156,3990,1110],{},[1172,3992,1110],{"encoding":1174},[1818,3994,1821,3996],{"id":3995},"diagram-cc",[1115,3997,3999],{"className":3998},[1136],[1138,4000,4001],{"xmlns":1140},[1142,4002,4003,4007],{},[1145,4004,4005],{},[1156,4006,1262],{},[1172,4008,1262],{"encoding":1174},[1110,4010,4011,4012,4030,4031,4044,4045,4070,4071,4084],{},"Regulovanou veličinou ",[1115,4013,4015],{"className":4014},[1136],[1138,4016,4017],{"xmlns":1140},[1142,4018,4019,4027],{},[1145,4020,4021],{},[1217,4022,4023,4025],{},[1156,4024,1262],{},[1156,4026,1223],{},[1172,4028,4029],{"encoding":1174},"c_i"," je počet neshod na produktech v ",[1115,4032,4034],{"className":4033},[1136],[1138,4035,4036],{"xmlns":1140},[1142,4037,4038,4042],{},[1145,4039,4040],{},[1156,4041,1223],{},[1172,4043,1223],{"encoding":1174},"-té logické podskupině, ",[1115,4046,4048],{"className":4047},[1136],[1138,4049,4050],{"xmlns":1140},[1142,4051,4052,4068],{},[1145,4053,4054,4056,4058,4060,4062,4064,4066],{},[1156,4055,1223],{},[1148,4057,1914],{},[1919,4059,1921],{},[1148,4061,1164],{"separator":1121},[1148,4063,2043],{},[1148,4065,1164],{"separator":1121},[1156,4067,1234],{},[1172,4069,2050],{"encoding":1174},"; v každé podskupině je stejný počet ",[1115,4072,4074],{"className":4073},[1136],[1138,4075,4076],{"xmlns":1140},[1142,4077,4078,4082],{},[1145,4079,4080],{},[1156,4081,1292],{},[1172,4083,1292],{"encoding":1174}," produktů. Počet neshod má Poissonovo rozdělení, pokud může být počet neshod na produktu teoreticky neohraničený a pravděpodobnost více než jedné neshody v určitém místě produktu je zanedbatelná.",[1103,4086,4088,4095],{"className":4087,"dataCallout":2145},[1106,2144],[1110,4089,4091,4094],{"className":4090},[1113],[1115,4092],{"className":4093,"ariaHidden":1121},[1118,2152,1120],"Příklad: bodové vady na pásech látky",[1110,4096,4097,4098,4115,4116,1247],{},"Při tkaní látek se zjišťuje počet bodových vad na pásech dlouhých 100 metrů. Pro 20 pásů v pořadí, v jakém byly vybrány, jsou dány počty vad ",[1115,4099,4101],{"className":4100},[1136],[1138,4102,4103],{"xmlns":1140},[1142,4104,4105,4113],{},[1145,4106,4107],{},[1217,4108,4109,4111],{},[1156,4110,1262],{},[1156,4112,1223],{},[1172,4114,4029],{"encoding":1174},". Sestrojte regulační diagram ",[1115,4117,4119],{"className":4118},[1136],[1138,4120,4121],{"xmlns":1140},[1142,4122,4123,4127],{},[1145,4124,4125],{},[1156,4126,1262],{},[1172,4128,1262],{"encoding":1174},[3261,4130,4132],{"className":3263,"code":4131,"language":71,"meta":3265,"style":3265},"c_i \u003C- c(7, 1, 2, 5, 0, 6, 2, 0, 4, 4, 6, 3, 3, 3, 1, 6, 3, 1, 5, 6)\n\nq_c \u003C- qcc(c_i, type = \"c\")\nsummary(q_c)\n",[1434,4133,4134,4232,4238,4263],{"__ignoreMap":3265},[1115,4135,4136,4138,4140,4143,4145,4148,4150,4152,4154,4157,4159,4162,4164,4167,4169,4172,4174,4176,4178,4180,4182,4185,4187,4189,4191,4193,4195,4198,4200,4202,4204,4206,4208,4210,4212,4214,4216,4218,4220,4222,4224,4226,4228,4230],{"class":3270,"line":10},[1115,4137,4029],{"class":3280},[1115,4139,3291],{"class":3273},[1115,4141,4142],{"class":3294}," c",[1115,4144,1151],{"class":3277},[1115,4146,4147],{"class":3312},"7",[1115,4149,1164],{"class":3273},[1115,4151,3882],{"class":3312},[1115,4153,1164],{"class":3273},[1115,4155,4156],{"class":3312}," 2",[1115,4158,1164],{"class":3273},[1115,4160,4161],{"class":3312}," 5",[1115,4163,1164],{"class":3273},[1115,4165,4166],{"class":3312}," 0",[1115,4168,1164],{"class":3273},[1115,4170,4171],{"class":3312}," 6",[1115,4173,1164],{"class":3273},[1115,4175,4156],{"class":3312},[1115,4177,1164],{"class":3273},[1115,4179,4166],{"class":3312},[1115,4181,1164],{"class":3273},[1115,4183,4184],{"class":3312}," 4",[1115,4186,1164],{"class":3273},[1115,4188,4184],{"class":3312},[1115,4190,1164],{"class":3273},[1115,4192,4171],{"class":3312},[1115,4194,1164],{"class":3273},[1115,4196,4197],{"class":3312}," 3",[1115,4199,1164],{"class":3273},[1115,4201,4197],{"class":3312},[1115,4203,1164],{"class":3273},[1115,4205,4197],{"class":3312},[1115,4207,1164],{"class":3273},[1115,4209,3882],{"class":3312},[1115,4211,1164],{"class":3273},[1115,4213,4171],{"class":3312},[1115,4215,1164],{"class":3273},[1115,4217,4197],{"class":3312},[1115,4219,1164],{"class":3273},[1115,4221,3882],{"class":3312},[1115,4223,1164],{"class":3273},[1115,4225,4161],{"class":3312},[1115,4227,1164],{"class":3273},[1115,4229,4171],{"class":3312},[1115,4231,3283],{"class":3277},[1115,4233,4234],{"class":3270,"line":27},[1115,4235,4237],{"emptyLinePlaceholder":4236},true,"\n",[1115,4239,4240,4243,4245,4248,4250,4252,4254,4256,4258,4261],{"class":3270,"line":148},[1115,4241,4242],{"class":3280},"q_c",[1115,4244,3291],{"class":3273},[1115,4246,4247],{"class":3294}," qcc",[1115,4249,1151],{"class":3277},[1115,4251,4029],{"class":3280},[1115,4253,1164],{"class":3273},[1115,4255,3328],{"class":3280},[1115,4257,3309],{"class":3273},[1115,4259,4260],{"class":3300}," \"c\"",[1115,4262,3283],{"class":3277},[1115,4264,4265,4268,4270,4272],{"class":3270,"line":111},[1115,4266,4267],{"class":3294},"summary",[1115,4269,1151],{"class":3277},[1115,4271,4242],{"class":3280},[1115,4273,3283],{"class":3277},[3261,4275,4280],{"className":4276,"code":4278,"language":4279,"meta":3265},[4277],"language-text","Call:\nqcc(data = c_i, type = \"c\")\n\nc chart for c_i \n\nSummary of group statistics:\n   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n   0.00    1.75    3.00    3.40    5.25    7.00 \n\nGroup sample size:  1\nNumber of groups:  20\nCenter of group statistics:  3.4\nStandard deviation:  1.843909 \n\nControl limits:\n LCL      UCL\n   0 8.931727\n","text",[1434,4281,4278],{"__ignoreMap":3265},[1110,4283,4284,4285,4314,4315,4338,4339,4361],{},"Průměrný počet vad na pás je ",[1115,4286,4288],{"className":4287},[1136],[1138,4289,4290],{"xmlns":1140},[1142,4291,4292,4311],{},[1145,4293,4294,4296,4298,4300,4306,4308],{},[1156,4295,1332],{},[1156,4297,2710],{},[1148,4299,1914],{},[1153,4301,4302,4304],{"accent":1121},[1156,4303,1262],{},[1148,4305,1161],{},[1148,4307,1914],{},[1919,4309,4310],{},"3,4",[1172,4312,4313],{"encoding":1174},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,4316,4318],{"className":4317},[1136],[1138,4319,4320],{"xmlns":1140},[1142,4321,4322,4335],{},[1145,4323,4324,4326,4328,4330,4332],{},[1156,4325,2736],{},[1156,4327,1332],{},[1156,4329,2710],{},[1148,4331,1914],{},[1919,4333,4334],{},"8,93",[1172,4336,4337],{"encoding":1174},"UCL = 8{,}93"," a dolní mez ",[1115,4340,4342],{"className":4341},[1136],[1138,4343,4344],{"xmlns":1140},[1142,4345,4346,4358],{},[1145,4347,4348,4350,4352,4354,4356],{},[1156,4349,2710],{},[1156,4351,1332],{},[1156,4353,2710],{},[1148,4355,1914],{},[1919,4357,2780],{},[1172,4359,4360],{"encoding":1174},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,4363,4364],{},[1527,4365],{"alt":4366,"className":4367,"src":4368},"mask-rd-priklad2-c",[1531,1532],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[1818,4370,1821,4372],{"id":4371},"diagram-uu",[1115,4373,4375],{"className":4374},[1136],[1138,4376,4377],{"xmlns":1140},[1142,4378,4379,4383],{},[1145,4380,4381],{},[1156,4382,1277],{},[1172,4384,1277],{"encoding":1174},[1110,4386,4011,4387,4422,4423,4441],{},[1115,4388,4390],{"className":4389},[1136],[1138,4391,4392],{"xmlns":1140},[1142,4393,4394,4419],{},[1145,4395,4396,4402,4404,4410,4413],{},[1217,4397,4398,4400],{},[1156,4399,1277],{},[1156,4401,1223],{},[1148,4403,1914],{},[1217,4405,4406,4408],{},[1156,4407,1262],{},[1156,4409,1223],{},[1156,4411,4412],{"mathvariant":2014},"\u002F",[1217,4414,4415,4417],{},[1156,4416,1292],{},[1156,4418,1223],{},[1172,4420,4421],{"encoding":1174},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,4424,4426],{"className":4425},[1136],[1138,4427,4428],{"xmlns":1140},[1142,4429,4430,4438],{},[1145,4431,4432],{},[1217,4433,4434,4436],{},[1156,4435,1292],{},[1156,4437,1223],{},[1172,4439,4440],{"encoding":1174},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,4443,4444,4445,4448],{},"Za ",[1434,4446,4447],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3261,4450,4452],{"className":3263,"code":4451,"language":71,"meta":3265,"style":3265},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[1434,4453,4454,4480],{"__ignoreMap":3265},[1115,4455,4456,4458,4460,4462,4464,4467,4469,4471,4473,4475,4477],{"class":3270,"line":10},[1115,4457,3288],{"class":3280},[1115,4459,3291],{"class":3273},[1115,4461,3295],{"class":3294},[1115,4463,1151],{"class":3277},[1115,4465,4466],{"class":3300},"\"3_4.txt\"",[1115,4468,1164],{"class":3273},[1115,4470,3306],{"class":3280},[1115,4472,3309],{"class":3273},[1115,4474,3313],{"class":3312},[1115,4476,3360],{"class":3277},[1115,4478,4479],{"class":3339},"# počty suků a rozměry prken\n",[1115,4481,4482,4484,4486,4488,4490,4492,4494,4496,4498,4500,4502,4505,4507,4510,4512,4515,4517,4519,4521],{"class":3270,"line":27},[1115,4483,360],{"class":3294},[1115,4485,1151],{"class":3277},[1115,4487,3288],{"class":3280},[1115,4489,3877],{"class":3277},[1115,4491,1164],{"class":3273},[1115,4493,3882],{"class":3312},[1115,4495,3885],{"class":3277},[1115,4497,1164],{"class":3273},[1115,4499,3328],{"class":3280},[1115,4501,3309],{"class":3273},[1115,4503,4504],{"class":3300}," \"u\"",[1115,4506,1164],{"class":3273},[1115,4508,4509],{"class":3280}," sizes",[1115,4511,3309],{"class":3273},[1115,4513,4514],{"class":3280}," data",[1115,4516,3877],{"class":3277},[1115,4518,1164],{"class":3273},[1115,4520,4156],{"class":3312},[1115,4522,4523],{"class":3277},"])\n",[1818,4525,1821,4527],{"id":4526},"diagram-npnp",[1115,4528,4530],{"className":4529},[1136],[1138,4531,4532],{"xmlns":1140},[1142,4533,4534,4540],{},[1145,4535,4536,4538],{},[1156,4537,1292],{},[1156,4539,1110],{},[1172,4541,1297],{"encoding":1174},[1110,4543,4544,4545,4560,4561,4574],{},"Regulovanou veličinou je počet neshodných produktů (ne neshod) v logické podskupině. Podmínky použití: rozsahy podskupin jsou stejně velké a velké (alespoň 50 produktů). Počet neshodných produktů má pak přibližně binomické rozdělení se střední hodnotou ",[1115,4546,4548],{"className":4547},[1136],[1138,4549,4550],{"xmlns":1140},[1142,4551,4552,4558],{},[1145,4553,4554,4556],{},[1156,4555,1292],{},[1156,4557,1110],{},[1172,4559,1297],{"encoding":1174},", kde ",[1115,4562,4564],{"className":4563},[1136],[1138,4565,4566],{"xmlns":1140},[1142,4567,4568,4572],{},[1145,4569,4570],{},[1156,4571,1110],{},[1172,4573,1110],{"encoding":1174}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,4576,4577,4578,2529],{},"Pro konstantní rozsah ",[1115,4579,4581],{"className":4580},[1136],[1138,4582,4583],{"xmlns":1140},[1142,4584,4585,4589],{},[1145,4586,4587],{},[1156,4588,1292],{},[1172,4590,1292],{"encoding":1174},[3261,4592,4594],{"className":3263,"code":4593,"language":71,"meta":3265,"style":3265},"data \u003C- read.table(\"3_7.txt\", header = TRUE)   # počty vadných tabletů v sériích po 100 kusech\nqcc(data[, 1], type = \"np\", sizes = 100)\n",[1434,4595,4596,4622],{"__ignoreMap":3265},[1115,4597,4598,4600,4602,4604,4606,4609,4611,4613,4615,4617,4619],{"class":3270,"line":10},[1115,4599,3288],{"class":3280},[1115,4601,3291],{"class":3273},[1115,4603,3295],{"class":3294},[1115,4605,1151],{"class":3277},[1115,4607,4608],{"class":3300},"\"3_7.txt\"",[1115,4610,1164],{"class":3273},[1115,4612,3306],{"class":3280},[1115,4614,3309],{"class":3273},[1115,4616,3313],{"class":3312},[1115,4618,3360],{"class":3277},[1115,4620,4621],{"class":3339},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,4623,4624,4626,4628,4630,4632,4634,4636,4638,4640,4642,4644,4647,4649,4651,4653,4656],{"class":3270,"line":27},[1115,4625,360],{"class":3294},[1115,4627,1151],{"class":3277},[1115,4629,3288],{"class":3280},[1115,4631,3877],{"class":3277},[1115,4633,1164],{"class":3273},[1115,4635,3882],{"class":3312},[1115,4637,3885],{"class":3277},[1115,4639,1164],{"class":3273},[1115,4641,3328],{"class":3280},[1115,4643,3309],{"class":3273},[1115,4645,4646],{"class":3300}," \"np\"",[1115,4648,1164],{"class":3273},[1115,4650,4509],{"class":3280},[1115,4652,3309],{"class":3273},[1115,4654,4655],{"class":3312}," 100",[1115,4657,3283],{"class":3277},[1818,4659,1821,4661],{"id":4660},"diagram-pp",[1115,4662,4664],{"className":4663},[1136],[1138,4665,4666],{"xmlns":1140},[1142,4667,4668,4672],{},[1145,4669,4670],{},[1156,4671,1110],{},[1172,4673,1110],{"encoding":1174},[1110,4675,4676,4677,4713],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,4678,4680],{"className":4679},[1136],[1138,4681,4682],{"xmlns":1140},[1142,4683,4684,4710],{},[1145,4685,4686,4692,4694,4696,4702,4704],{},[1217,4687,4688,4690],{},[1156,4689,1110],{},[1156,4691,1223],{},[1148,4693,1914],{},[1156,4695,1292],{},[1217,4697,4698,4700],{},[1156,4699,1110],{},[1156,4701,1223],{},[1156,4703,4412],{"mathvariant":2014},[1217,4705,4706,4708],{},[1156,4707,1292],{},[1156,4709,1223],{},[1172,4711,4712],{"encoding":1174},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,4715,4444,4716,4718],{},[1434,4717,4447],{}," se dosadí vektor rozsahů logických podskupin:",[3261,4720,4722],{"className":3263,"code":4721,"language":71,"meta":3265,"style":3265},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[1434,4723,4724,4750],{"__ignoreMap":3265},[1115,4725,4726,4728,4730,4732,4734,4737,4739,4741,4743,4745,4747],{"class":3270,"line":10},[1115,4727,3288],{"class":3280},[1115,4729,3291],{"class":3273},[1115,4731,3295],{"class":3294},[1115,4733,1151],{"class":3277},[1115,4735,4736],{"class":3300},"\"3_6.txt\"",[1115,4738,1164],{"class":3273},[1115,4740,3306],{"class":3280},[1115,4742,3309],{"class":3273},[1115,4744,3313],{"class":3312},[1115,4746,3360],{"class":3277},[1115,4748,4749],{"class":3339},"# počty vadných tabletů a rozsahy sérií\n",[1115,4751,4752,4754,4756,4758,4760,4762,4764,4766,4768,4770,4772,4775,4777,4779,4781,4783,4785,4787,4789],{"class":3270,"line":27},[1115,4753,360],{"class":3294},[1115,4755,1151],{"class":3277},[1115,4757,3288],{"class":3280},[1115,4759,3877],{"class":3277},[1115,4761,1164],{"class":3273},[1115,4763,3882],{"class":3312},[1115,4765,3885],{"class":3277},[1115,4767,1164],{"class":3273},[1115,4769,3328],{"class":3280},[1115,4771,3309],{"class":3273},[1115,4773,4774],{"class":3300}," \"p\"",[1115,4776,1164],{"class":3273},[1115,4778,4509],{"class":3280},[1115,4780,3309],{"class":3273},[1115,4782,4514],{"class":3280},[1115,4784,3877],{"class":3277},[1115,4786,1164],{"class":3273},[1115,4788,4156],{"class":3312},[1115,4790,4523],{"class":3277},[1437,4792,4794],{"id":4793},"indexy-způsobilosti","Indexy způsobilosti",[1110,4796,4797,4798,4817,4818,4836],{},"Zatímco regulační diagram posuzuje stabilitu procesu v čase, index způsobilosti posuzuje, zda se zvládnutý proces svou přirozenou variabilitou vejde do tolerančních mezí zadaných specifikací — dolní meze ",[1115,4799,4801],{"className":4800},[1136],[1138,4802,4803],{"xmlns":1140},[1142,4804,4805,4814],{},[1145,4806,4807,4809,4812],{},[1156,4808,2710],{},[1156,4810,4811],{},"S",[1156,4813,2710],{},[1172,4815,4816],{"encoding":1174},"LSL"," a horní meze ",[1115,4819,4821],{"className":4820},[1136],[1138,4822,4823],{"xmlns":1140},[1142,4824,4825,4833],{},[1145,4826,4827,4829,4831],{},[1156,4828,2736],{},[1156,4830,4811],{},[1156,4832,2710],{},[1172,4834,4835],{"encoding":1174},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[1818,4838,4840,4857],{"id":4839},"cpc_p-index-způsobilosti",[1115,4841,4843],{"className":4842},[1136],[1138,4844,4845],{"xmlns":1140},[1142,4846,4847,4855],{},[1145,4848,4849],{},[1217,4850,4851,4853],{},[1156,4852,1332],{},[1156,4854,1110],{},[1172,4856,1337],{"encoding":1174}," — index způsobilosti",[1110,4859,4860,4861,2529],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,4862,4864],{"className":4863},[1136],[1138,4865,4866],{"xmlns":1140},[1142,4867,4868,4874],{},[1145,4869,4870,4872],{},[1919,4871,2437],{},[1156,4873,1693],{},[1172,4875,4876],{"encoding":1174},"6\\sigma",[1115,4878,4880],{"className":4879},[1136],[1138,4881,4882],{"xmlns":1140,"display":1897},[1142,4883,4884,4920],{},[1145,4885,4886,4892,4894,4918],{},[1217,4887,4888,4890],{},[1156,4889,1332],{},[1156,4891,1110],{},[1148,4893,1914],{},[1916,4895,4896,4912],{},[1145,4897,4898,4900,4902,4904,4906,4908,4910],{},[1156,4899,2736],{},[1156,4901,4811],{},[1156,4903,2710],{},[1148,4905,1990],{},[1156,4907,2710],{},[1156,4909,4811],{},[1156,4911,2710],{},[1145,4913,4914,4916],{},[1919,4915,2437],{},[1156,4917,1693],{},[1156,4919,1247],{"mathvariant":2014},[1172,4921,4922],{"encoding":1174},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,4924,4925,4942,4943,4956,4957,1247],{},[1115,4926,4928],{"className":4927},[1136],[1138,4929,4930],{"xmlns":1140},[1142,4931,4932,4940],{},[1145,4933,4934],{},[1217,4935,4936,4938],{},[1156,4937,1332],{},[1156,4939,1110],{},[1172,4941,1337],{"encoding":1174}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,4944,4946],{"className":4945},[1136],[1138,4947,4948],{"xmlns":1140},[1142,4949,4950,4954],{},[1145,4951,4952],{},[1156,4953,1693],{},[1172,4955,1696],{"encoding":1174}," mají stejné ",[1115,4958,4960],{"className":4959},[1136],[1138,4961,4962],{"xmlns":1140},[1142,4963,4964,4972],{},[1145,4965,4966],{},[1217,4967,4968,4970],{},[1156,4969,1332],{},[1156,4971,1110],{},[1172,4973,1337],{"encoding":1174},[1110,4975,4976],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1124,4978,4979,5019,5108],{},[1127,4980,4981,4984,4985,5018],{},[1445,4982,4983],{},"míra využití tolerančního intervalu",": ",[1115,4986,4988],{"className":4987},[1136],[1138,4989,4990],{"xmlns":1140},[1142,4991,4992,5015],{},[1145,4993,4994,5008,5012],{},[4995,4996,4997],"mstyle",{"scriptlevel":2780,"displaystyle":1121},[1916,4998,4999,5002],{},[1919,5000,5001],{},"100",[1217,5003,5004,5006],{},[1156,5005,1332],{},[1156,5007,1110],{},[5009,5010,5011],"mtext",{}," ",[1156,5013,5014],{"mathvariant":2014},"%",[1172,5016,5017],{"encoding":1174},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1127,5020,5021,5024,5025,5042,5043,1204,5076,1164],{},[1445,5022,5023],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,5026,5028],{"className":5027},[1136],[1138,5029,5030],{"xmlns":1140},[1142,5031,5032,5040],{},[1145,5033,5034],{},[1217,5035,5036,5038],{},[1156,5037,1332],{},[1156,5039,1110],{},[1172,5041,1337],{"encoding":1174}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,5044,5046],{"className":5045},[1136],[1138,5047,5048],{"xmlns":1140},[1142,5049,5050,5073],{},[1145,5051,5052,5054,5056,5058,5060,5062,5064,5067,5069,5071],{},[1156,5053,2736],{},[1156,5055,4811],{},[1156,5057,2710],{},[1148,5059,1990],{},[1148,5061,1151],{"stretchy":1150},[1156,5063,1677],{},[1148,5065,5066],{},"+",[1919,5068,2327],{},[1156,5070,1693],{},[1148,5072,1170],{"stretchy":1150},[1172,5074,5075],{"encoding":1174},"USL-(\\mu+3\\sigma)",[1115,5077,5079],{"className":5078},[1136],[1138,5080,5081],{"xmlns":1140},[1142,5082,5083,5105],{},[1145,5084,5085,5087,5089,5091,5093,5095,5097,5099,5101,5103],{},[1148,5086,1151],{"stretchy":1150},[1156,5088,1677],{},[1148,5090,1990],{},[1919,5092,2327],{},[1156,5094,1693],{},[1148,5096,1170],{"stretchy":1150},[1148,5098,1990],{},[1156,5100,2710],{},[1156,5102,4811],{},[1156,5104,2710],{},[1172,5106,5107],{"encoding":1174},"(\\mu-3\\sigma)-LSL",[1127,5109,5110,4984,5113,4560,5154,5168],{},[1445,5111,5112],{},"podíl zmetků",[1115,5114,5116],{"className":5115},[1136],[1138,5117,5118],{"xmlns":1140},[1142,5119,5120,5151],{},[1145,5121,5122,5130,5132,5134,5137,5139,5141,5143,5149],{},[1217,5123,5124,5127],{},[1156,5125,5126],{},"P",[1156,5128,5129],{},"z",[1148,5131,1914],{},[1919,5133,2302],{},[1156,5135,5136],{"mathvariant":2014},"Φ",[1148,5138,1151],{"stretchy":1150},[1148,5140,1990],{},[1919,5142,2327],{},[1217,5144,5145,5147],{},[1156,5146,1332],{},[1156,5148,1110],{},[1148,5150,1170],{"stretchy":1150},[1172,5152,5153],{"encoding":1174},"P_z = 2\\Phi(-3C_p)",[1115,5155,5157],{"className":5156},[1136],[1138,5158,5159],{"xmlns":1140},[1142,5160,5161,5165],{},[1145,5162,5163],{},[1156,5164,5136],{"mathvariant":2014},[1172,5166,5167],{"encoding":1174},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[1818,5170,5172,5193],{"id":5171},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,5173,5175],{"className":5174},[1136],[1138,5176,5177],{"xmlns":1140},[1142,5178,5179,5191],{},[1145,5180,5181],{},[1217,5182,5183,5185],{},[1156,5184,1332],{},[1145,5186,5187,5189],{},[1156,5188,1110],{},[1156,5190,1234],{},[1172,5192,1359],{"encoding":1174}," — index způsobilosti s ohledem na vychýlení",[1110,5195,5196],{},"Bere v úvahu, že proces nemusí být centrovaný na střed tolerance; počítá se samostatně vzdálenost k horní a dolní mezi a horší z obou se stane indexem:",[1115,5198,5200],{"className":5199},[1136],[1138,5201,5202],{"xmlns":1140,"display":1897},[1142,5203,5204,5275],{},[1145,5205,5206,5216,5218,5220,5222,5273],{},[1217,5207,5208,5210],{},[1156,5209,1332],{},[1145,5211,5212,5214],{},[1156,5213,1110],{},[1156,5215,1234],{},[1148,5217,1914],{},[1156,5219,1997],{},[1148,5221,1975],{},[1145,5223,5224,5226,5246,5248,5251,5271],{},[1148,5225,1151],{"fence":1121},[1916,5227,5228,5240],{},[1145,5229,5230,5232,5234,5236,5238],{},[1156,5231,2736],{},[1156,5233,4811],{},[1156,5235,2710],{},[1148,5237,1990],{},[1156,5239,1677],{},[1145,5241,5242,5244],{},[1919,5243,2327],{},[1156,5245,1693],{},[1148,5247,1164],{"separator":1121},[5009,5249,5250],{}," ",[1916,5252,5253,5265],{},[1145,5254,5255,5257,5259,5261,5263],{},[1156,5256,1677],{},[1148,5258,1990],{},[1156,5260,2710],{},[1156,5262,4811],{},[1156,5264,2710],{},[1145,5266,5267,5269],{},[1919,5268,2327],{},[1156,5270,1693],{},[1148,5272,1170],{"fence":1121},[1156,5274,1247],{"mathvariant":2014},[1172,5276,5277],{"encoding":1174},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,5279,5280,5281,5294,5295,5325,5326,5347,5348,1247],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,5282,5284],{"className":5283},[1136],[1138,5285,5286],{"xmlns":1140},[1142,5287,5288,5292],{},[1145,5289,5290],{},[1156,5291,1677],{},[1172,5293,1680],{"encoding":1174}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,5296,5298],{"className":5297},[1136],[1138,5299,5300],{"xmlns":1140},[1142,5301,5302,5322],{},[1145,5303,5304,5314,5316],{},[1217,5305,5306,5308],{},[1156,5307,1332],{},[1145,5309,5310,5312],{},[1156,5311,1110],{},[1156,5313,1234],{},[1148,5315,1914],{},[1217,5317,5318,5320],{},[1156,5319,1332],{},[1156,5321,1110],{},[1172,5323,5324],{"encoding":1174},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,5327,5329],{"className":5328},[1136],[1138,5330,5331],{"xmlns":1140},[1142,5332,5333,5345],{},[1145,5334,5335],{},[1217,5336,5337,5339],{},[1156,5338,1332],{},[1145,5340,5341,5343],{},[1156,5342,1110],{},[1156,5344,1234],{},[1172,5346,1359],{"encoding":1174}," menší než ",[1115,5349,5351],{"className":5350},[1136],[1138,5352,5353],{"xmlns":1140},[1142,5354,5355,5363],{},[1145,5356,5357],{},[1217,5358,5359,5361],{},[1156,5360,1332],{},[1156,5362,1110],{},[1172,5364,1337],{"encoding":1174},[1818,5366,5368,1204,5389,5412],{"id":5367},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,5369,5371],{"className":5370},[1136],[1138,5372,5373],{"xmlns":1140},[1142,5374,5375,5387],{},[1145,5376,5377],{},[1217,5378,5379,5381],{},[1156,5380,1332],{},[1145,5382,5383,5385],{},[1156,5384,1110],{},[1156,5386,1379],{},[1172,5388,1382],{"encoding":1174},[1115,5390,5392],{"className":5391},[1136],[1138,5393,5394],{"xmlns":1140},[1142,5395,5396,5410],{},[1145,5397,5398],{},[1217,5399,5400,5402],{},[1156,5401,1332],{},[1145,5403,5404,5406,5408],{},[1156,5405,1110],{},[1156,5407,1379],{},[1156,5409,1234],{},[1172,5411,1406],{"encoding":1174}," — indexy vztažené k cíli",[1110,5414,5415,5416,5430,5431,5444,5445,5490,5491,2529],{},"Pokud má proces zadaný cílový střed ",[1115,5417,5419],{"className":5418},[1136],[1138,5420,5421],{"xmlns":1140},[1142,5422,5423,5428],{},[1145,5424,5425],{},[1156,5426,5427],{},"T",[1172,5429,5427],{"encoding":1174}," (ne nutně střed tolerance), nahradí se ",[1115,5432,5434],{"className":5433},[1136],[1138,5435,5436],{"xmlns":1140},[1142,5437,5438,5442],{},[1145,5439,5440],{},[1156,5441,1693],{},[1172,5443,1696],{"encoding":1174}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,5446,5448],{"className":5447},[1136],[1138,5449,5450],{"xmlns":1140},[1142,5451,5452,5487],{},[1145,5453,5454,5457,5459],{},[1156,5455,5456],{},"τ",[1148,5458,1914],{},[5460,5461,5462],"msqrt",{},[1145,5463,5464,5471,5473,5475,5477,5479,5481],{},[5465,5466,5467,5469],"msup",{},[1156,5468,1693],{},[1919,5470,2302],{},[1148,5472,5066],{},[1148,5474,1151],{"stretchy":1150},[1156,5476,1677],{},[1148,5478,1990],{},[1156,5480,5427],{},[5465,5482,5483,5485],{},[1148,5484,1170],{"stretchy":1150},[1919,5486,2302],{},[1172,5488,5489],{"encoding":1174},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,5492,5494],{"className":5493},[1136],[1138,5495,5496],{"xmlns":1140},[1142,5497,5498,5502],{},[1145,5499,5500],{},[1156,5501,5427],{},[1172,5503,5427],{"encoding":1174},[1115,5505,5507],{"className":5506},[1136],[1138,5508,5509],{"xmlns":1140,"display":1897},[1142,5510,5511,5623],{},[1145,5512,5513,5523,5525,5549,5551,5553,5565,5567,5569,5571,5621],{},[1217,5514,5515,5517],{},[1156,5516,1332],{},[1145,5518,5519,5521],{},[1156,5520,1110],{},[1156,5522,1379],{},[1148,5524,1914],{},[1916,5526,5527,5543],{},[1145,5528,5529,5531,5533,5535,5537,5539,5541],{},[1156,5530,2736],{},[1156,5532,4811],{},[1156,5534,2710],{},[1148,5536,1990],{},[1156,5538,2710],{},[1156,5540,4811],{},[1156,5542,2710],{},[1145,5544,5545,5547],{},[1919,5546,2437],{},[1156,5548,5456],{},[1148,5550,1164],{"separator":1121},[1954,5552],{"width":1956},[1217,5554,5555,5557],{},[1156,5556,1332],{},[1145,5558,5559,5561,5563],{},[1156,5560,1110],{},[1156,5562,1379],{},[1156,5564,1234],{},[1148,5566,1914],{},[1156,5568,1997],{},[1148,5570,1975],{},[1145,5572,5573,5575,5595,5597,5599,5619],{},[1148,5574,1151],{"fence":1121},[1916,5576,5577,5589],{},[1145,5578,5579,5581,5583,5585,5587],{},[1156,5580,2736],{},[1156,5582,4811],{},[1156,5584,2710],{},[1148,5586,1990],{},[1156,5588,1677],{},[1145,5590,5591,5593],{},[1919,5592,2327],{},[1156,5594,5456],{},[1148,5596,1164],{"separator":1121},[5009,5598,5250],{},[1916,5600,5601,5613],{},[1145,5602,5603,5605,5607,5609,5611],{},[1156,5604,1677],{},[1148,5606,1990],{},[1156,5608,2710],{},[1156,5610,4811],{},[1156,5612,2710],{},[1145,5614,5615,5617],{},[1919,5616,2327],{},[1156,5618,5456],{},[1148,5620,1170],{"fence":1121},[1156,5622,1247],{"mathvariant":2014},[1172,5624,5625],{"encoding":1174},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[1818,5627,5629],{"id":5628},"interpretace","Interpretace",[1459,5631,5632,5659],{},[1462,5633,5634],{},[1465,5635,5636,5656],{},[1468,5637,5638,5639],{},"Hodnota ",[1115,5640,5642],{"className":5641},[1136],[1138,5643,5644],{"xmlns":1140},[1142,5645,5646,5654],{},[1145,5647,5648],{},[1217,5649,5650,5652],{},[1156,5651,1332],{},[1156,5653,1110],{},[1172,5655,1337],{"encoding":1174},[1468,5657,5658],{},"Způsobilost procesu",[1477,5660,5661,5691,5734],{},[1465,5662,5663,5688],{},[1482,5664,5665],{},[1115,5666,5668],{"className":5667},[1136],[1138,5669,5670],{"xmlns":1140},[1142,5671,5672,5685],{},[1145,5673,5674,5680,5683],{},[1217,5675,5676,5678],{},[1156,5677,1332],{},[1156,5679,1110],{},[1148,5681,5682],{},"\u003C",[1919,5684,1921],{},[1172,5686,5687],{"encoding":1174},"C_p \u003C 1",[1482,5689,5690],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1465,5692,5693,5717],{},[1482,5694,5695],{},[1115,5696,5698],{"className":5697},[1136],[1138,5699,5700],{"xmlns":1140},[1142,5701,5702,5714],{},[1145,5703,5704,5710,5712],{},[1217,5705,5706,5708],{},[1156,5707,1332],{},[1156,5709,1110],{},[1148,5711,1914],{},[1919,5713,1921],{},[1172,5715,5716],{"encoding":1174},"C_p = 1",[1482,5718,5719,5720,5733],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,5721,5723],{"className":5722},[1136],[1138,5724,5725],{"xmlns":1140},[1142,5726,5727,5731],{},[1145,5728,5729],{},[1156,5730,1693],{},[1172,5732,1696],{"encoding":1174}," jej posune na nezpůsobilý",[1465,5735,5736,5761],{},[1482,5737,5738],{},[1115,5739,5741],{"className":5740},[1136],[1138,5742,5743],{"xmlns":1140},[1142,5744,5745,5758],{},[1145,5746,5747,5753,5756],{},[1217,5748,5749,5751],{},[1156,5750,1332],{},[1156,5752,1110],{},[1148,5754,5755],{},">",[1919,5757,1921],{},[1172,5759,5760],{"encoding":1174},"C_p > 1",[1482,5762,5763],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,5765,5766,5767,5788,5789,1247],{},"U indexu ",[1115,5768,5770],{"className":5769},[1136],[1138,5771,5772],{"xmlns":1140},[1142,5773,5774,5786],{},[1145,5775,5776],{},[1217,5777,5778,5780],{},[1156,5779,1332],{},[1145,5781,5782,5784],{},[1156,5783,1110],{},[1156,5785,1234],{},[1172,5787,1359],{"encoding":1174}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,5790,5792],{"className":5791},[1136],[1138,5793,5794],{"xmlns":1140},[1142,5795,5796,5801],{},[1145,5797,5798],{},[1919,5799,5800],{},"1,5",[1172,5802,5803],{"encoding":1174},"1{,}5",[1110,5805,5806],{},[1527,5807],{"alt":5808,"className":5809,"src":5810},"mask-rd-cp-panely",[1531,1532],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,5812,5813],{},[1527,5814],{"alt":5815,"className":5816,"src":5817},"mask-rd-cpk-off-centre",[1531,1532],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[1818,5819,5821],{"id":5820},"výpočet-v-r","Výpočet v R",[1110,5823,5824,5825,5828,5829,5832,5833,5836,5837,1204,5854,1176,5871,5874,5875,5888],{},"Indexy způsobilosti počítá ",[1434,5826,5827],{},"process.capability()"," z výstupu regulačního diagramu ",[1434,5830,5831],{},"q","; ",[1434,5834,5835],{},"spec.limits"," jsou toleranční meze ",[1115,5838,5840],{"className":5839},[1136],[1138,5841,5842],{"xmlns":1140},[1142,5843,5844,5852],{},[1145,5845,5846,5848,5850],{},[1156,5847,2710],{},[1156,5849,4811],{},[1156,5851,2710],{},[1172,5853,4816],{"encoding":1174},[1115,5855,5857],{"className":5856},[1136],[1138,5858,5859],{"xmlns":1140},[1142,5860,5861,5869],{},[1145,5862,5863,5865,5867],{},[1156,5864,2736],{},[1156,5866,4811],{},[1156,5868,2710],{},[1172,5870,4835],{"encoding":1174},[1434,5872,5873],{},"target"," cílová hodnota ",[1115,5876,5878],{"className":5877},[1136],[1138,5879,5880],{"xmlns":1140},[1142,5881,5882,5886],{},[1145,5883,5884],{},[1156,5885,5427],{},[1172,5887,5427],{"encoding":1174},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3261,5890,5892],{"className":3263,"code":5891,"language":71,"meta":3265,"style":3265},"library(qcc)\ndata \u003C- read.table(\"3_8.txt\", header = TRUE)\nx \u003C- as.matrix(data)\nq \u003C- qcc(x, type = \"xbar\")\nprocess.capability(q, spec.limits = c(100, 110), target = 105, std.dev = sd(x))\n",[1434,5893,5894,5904,5927,5942,5964],{"__ignoreMap":3265},[1115,5895,5896,5898,5900,5902],{"class":3270,"line":10},[1115,5897,3274],{"class":3273},[1115,5899,1151],{"class":3277},[1115,5901,360],{"class":3280},[1115,5903,3283],{"class":3277},[1115,5905,5906,5908,5910,5912,5914,5917,5919,5921,5923,5925],{"class":3270,"line":27},[1115,5907,3288],{"class":3280},[1115,5909,3291],{"class":3273},[1115,5911,3295],{"class":3294},[1115,5913,1151],{"class":3277},[1115,5915,5916],{"class":3300},"\"3_8.txt\"",[1115,5918,1164],{"class":3273},[1115,5920,3306],{"class":3280},[1115,5922,3309],{"class":3273},[1115,5924,3313],{"class":3312},[1115,5926,3283],{"class":3277},[1115,5928,5929,5931,5933,5936,5938,5940],{"class":3270,"line":148},[1115,5930,1158],{"class":3280},[1115,5932,3291],{"class":3273},[1115,5934,5935],{"class":3294}," as.matrix",[1115,5937,1151],{"class":3277},[1115,5939,3288],{"class":3280},[1115,5941,3283],{"class":3277},[1115,5943,5944,5946,5948,5950,5952,5954,5956,5958,5960,5962],{"class":3270,"line":111},[1115,5945,5831],{"class":3280},[1115,5947,3291],{"class":3273},[1115,5949,4247],{"class":3294},[1115,5951,1151],{"class":3277},[1115,5953,1158],{"class":3280},[1115,5955,1164],{"class":3273},[1115,5957,3328],{"class":3280},[1115,5959,3309],{"class":3273},[1115,5961,3357],{"class":3300},[1115,5963,3283],{"class":3277},[1115,5965,5966,5969,5971,5973,5975,5978,5980,5982,5984,5986,5988,5991,5993,5995,5998,6000,6003,6005,6008,6010,6013,6015,6017],{"class":3270,"line":96},[1115,5967,5968],{"class":3294},"process.capability",[1115,5970,1151],{"class":3277},[1115,5972,5831],{"class":3280},[1115,5974,1164],{"class":3273},[1115,5976,5977],{"class":3280}," spec.limits",[1115,5979,3309],{"class":3273},[1115,5981,4142],{"class":3294},[1115,5983,1151],{"class":3277},[1115,5985,5001],{"class":3312},[1115,5987,1164],{"class":3273},[1115,5989,5990],{"class":3312}," 110",[1115,5992,1170],{"class":3277},[1115,5994,1164],{"class":3273},[1115,5996,5997],{"class":3280}," target",[1115,5999,3309],{"class":3273},[1115,6001,6002],{"class":3312}," 105",[1115,6004,1164],{"class":3273},[1115,6006,6007],{"class":3280}," std.dev",[1115,6009,3309],{"class":3273},[1115,6011,6012],{"class":3294}," sd",[1115,6014,1151],{"class":3277},[1115,6016,1158],{"class":3280},[1115,6018,6019],{"class":3277},"))\n",[1110,6021,6022,6023,1176,6026,1176,6029,1176,6032,1204,6035,6038,6039,1204,6041,6043,6044,6065,6066,6089],{},"Výpis obsahuje řádky ",[1434,6024,6025],{},"Cp",[1434,6027,6028],{},"Cp_l",[1434,6030,6031],{},"Cp_u",[1434,6033,6034],{},"Cp_k",[1434,6036,6037],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[1434,6040,6028],{},[1434,6042,6031],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,6045,6047],{"className":6046},[1136],[1138,6048,6049],{"xmlns":1140},[1142,6050,6051,6063],{},[1145,6052,6053],{},[1217,6054,6055,6057],{},[1156,6056,1332],{},[1145,6058,6059,6061],{},[1156,6060,1110],{},[1156,6062,1234],{},[1172,6064,1359],{"encoding":1174},". Index ",[1115,6067,6069],{"className":6068},[1136],[1138,6070,6071],{"xmlns":1140},[1142,6072,6073,6087],{},[1145,6074,6075],{},[1217,6076,6077,6079],{},[1156,6078,1332],{},[1145,6080,6081,6083,6085],{},[1156,6082,1110],{},[1156,6084,1379],{},[1156,6086,1234],{},[1172,6088,1406],{"encoding":1174}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3261,6091,6093],{"className":3263,"code":6092,"language":71,"meta":3265,"style":3265},"mu \u003C- mean(x); sigma \u003C- sd(x)\nLSL \u003C- 100; USL \u003C- 110; T \u003C- 105\ntau \u003C- sqrt(sigma^2 + (mu - T)^2)\nCp \u003C- (USL - LSL) \u002F (6 * sigma)\nCpmk \u003C- min((USL - mu) \u002F (3 * tau), (mu - LSL) \u002F (3 * tau))\nmiravyuziti \u003C- 100 \u002F Cp\nrobustnost \u003C- min(USL - (mu + 3 * sigma), (mu - 3 * sigma) - LSL)\nPz \u003C- 2 * pnorm(-3 * Cp)\n",[1434,6094,6095,6124,6149,6190,6222,6281,6296,6348],{"__ignoreMap":3265},[1115,6096,6097,6100,6102,6105,6107,6109,6112,6114,6116,6118,6120,6122],{"class":3270,"line":10},[1115,6098,6099],{"class":3280},"mu",[1115,6101,3291],{"class":3273},[1115,6103,6104],{"class":3294}," mean",[1115,6106,1151],{"class":3277},[1115,6108,1158],{"class":3280},[1115,6110,6111],{"class":3277},"); ",[1115,6113,380],{"class":3280},[1115,6115,3291],{"class":3273},[1115,6117,6012],{"class":3294},[1115,6119,1151],{"class":3277},[1115,6121,1158],{"class":3280},[1115,6123,3283],{"class":3277},[1115,6125,6126,6128,6130,6132,6134,6136,6138,6140,6142,6144,6146],{"class":3270,"line":27},[1115,6127,4816],{"class":3280},[1115,6129,3291],{"class":3273},[1115,6131,4655],{"class":3312},[1115,6133,5832],{"class":3277},[1115,6135,4835],{"class":3280},[1115,6137,3291],{"class":3273},[1115,6139,5990],{"class":3312},[1115,6141,5832],{"class":3277},[1115,6143,5427],{"class":3280},[1115,6145,3291],{"class":3273},[1115,6147,6148],{"class":3312}," 105\n",[1115,6150,6151,6154,6156,6159,6161,6163,6166,6168,6171,6174,6176,6179,6182,6184,6186,6188],{"class":3270,"line":148},[1115,6152,6153],{"class":3280},"tau",[1115,6155,3291],{"class":3273},[1115,6157,6158],{"class":3294}," sqrt",[1115,6160,1151],{"class":3277},[1115,6162,380],{"class":3280},[1115,6164,6165],{"class":3273},"^",[1115,6167,2302],{"class":3312},[1115,6169,6170],{"class":3273}," +",[1115,6172,6173],{"class":3277}," (",[1115,6175,6099],{"class":3280},[1115,6177,6178],{"class":3273}," -",[1115,6180,6181],{"class":3280}," T",[1115,6183,1170],{"class":3277},[1115,6185,6165],{"class":3273},[1115,6187,2302],{"class":3312},[1115,6189,3283],{"class":3277},[1115,6191,6192,6194,6196,6198,6200,6202,6205,6208,6210,6212,6214,6217,6220],{"class":3270,"line":111},[1115,6193,6025],{"class":3280},[1115,6195,3291],{"class":3273},[1115,6197,6173],{"class":3277},[1115,6199,4835],{"class":3280},[1115,6201,6178],{"class":3273},[1115,6203,6204],{"class":3280}," LSL",[1115,6206,6207],{"class":3277},") ",[1115,6209,4412],{"class":3273},[1115,6211,6173],{"class":3277},[1115,6213,2437],{"class":3312},[1115,6215,6216],{"class":3273}," *",[1115,6218,6219],{"class":3280}," sigma",[1115,6221,3283],{"class":3277},[1115,6223,6224,6227,6229,6232,6235,6237,6239,6242,6244,6246,6248,6250,6252,6255,6257,6259,6261,6263,6265,6267,6269,6271,6273,6275,6277,6279],{"class":3270,"line":96},[1115,6225,6226],{"class":3280},"Cpmk",[1115,6228,3291],{"class":3273},[1115,6230,6231],{"class":3294}," min",[1115,6233,6234],{"class":3277},"((",[1115,6236,4835],{"class":3280},[1115,6238,6178],{"class":3273},[1115,6240,6241],{"class":3280}," mu",[1115,6243,6207],{"class":3277},[1115,6245,4412],{"class":3273},[1115,6247,6173],{"class":3277},[1115,6249,2327],{"class":3312},[1115,6251,6216],{"class":3273},[1115,6253,6254],{"class":3280}," tau",[1115,6256,1170],{"class":3277},[1115,6258,1164],{"class":3273},[1115,6260,6173],{"class":3277},[1115,6262,6099],{"class":3280},[1115,6264,6178],{"class":3273},[1115,6266,6204],{"class":3280},[1115,6268,6207],{"class":3277},[1115,6270,4412],{"class":3273},[1115,6272,6173],{"class":3277},[1115,6274,2327],{"class":3312},[1115,6276,6216],{"class":3273},[1115,6278,6254],{"class":3280},[1115,6280,6019],{"class":3277},[1115,6282,6283,6286,6288,6290,6293],{"class":3270,"line":89},[1115,6284,6285],{"class":3280},"miravyuziti",[1115,6287,3291],{"class":3273},[1115,6289,4655],{"class":3312},[1115,6291,6292],{"class":3273}," \u002F",[1115,6294,6295],{"class":3280}," Cp\n",[1115,6297,6298,6301,6303,6305,6307,6309,6311,6313,6315,6317,6319,6321,6323,6325,6327,6329,6331,6333,6335,6337,6339,6341,6344,6346],{"class":3270,"line":82},[1115,6299,6300],{"class":3280},"robustnost",[1115,6302,3291],{"class":3273},[1115,6304,6231],{"class":3294},[1115,6306,1151],{"class":3277},[1115,6308,4835],{"class":3280},[1115,6310,6178],{"class":3273},[1115,6312,6173],{"class":3277},[1115,6314,6099],{"class":3280},[1115,6316,6170],{"class":3273},[1115,6318,4197],{"class":3312},[1115,6320,6216],{"class":3273},[1115,6322,6219],{"class":3280},[1115,6324,1170],{"class":3277},[1115,6326,1164],{"class":3273},[1115,6328,6173],{"class":3277},[1115,6330,6099],{"class":3280},[1115,6332,6178],{"class":3273},[1115,6334,4197],{"class":3312},[1115,6336,6216],{"class":3273},[1115,6338,6219],{"class":3280},[1115,6340,6207],{"class":3277},[1115,6342,6343],{"class":3273},"-",[1115,6345,6204],{"class":3280},[1115,6347,3283],{"class":3277},[1115,6349,6350,6353,6355,6357,6359,6362,6364,6366,6368,6370,6373],{"class":3270,"line":75},[1115,6351,6352],{"class":3280},"Pz",[1115,6354,3291],{"class":3273},[1115,6356,4156],{"class":3312},[1115,6358,6216],{"class":3273},[1115,6360,6361],{"class":3294}," pnorm",[1115,6363,1151],{"class":3277},[1115,6365,6343],{"class":3273},[1115,6367,2327],{"class":3312},[1115,6369,6216],{"class":3273},[1115,6371,6372],{"class":3280}," Cp",[1115,6374,3283],{"class":3277},[1437,6376,6378],{"id":6377},"časté-chyby","Časté chyby",[1124,6380,6381,6384,6444,6535,6601],{},[1127,6382,6383],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1127,6385,6386,6387,6404,6405,6422,6423,1247],{},"Posuzovat jen ",[1115,6388,6390],{"className":6389},[1136],[1138,6391,6392],{"xmlns":1140},[1142,6393,6394,6402],{},[1145,6395,6396],{},[1217,6397,6398,6400],{},[1156,6399,1332],{},[1156,6401,1110],{},[1172,6403,1337],{"encoding":1174}," u vychýleného procesu — ",[1115,6406,6408],{"className":6407},[1136],[1138,6409,6410],{"xmlns":1140},[1142,6411,6412,6420],{},[1145,6413,6414],{},[1217,6415,6416,6418],{},[1156,6417,1332],{},[1156,6419,1110],{},[1172,6421,1337],{"encoding":1174}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,6424,6426],{"className":6425},[1136],[1138,6427,6428],{"xmlns":1140},[1142,6429,6430,6442],{},[1145,6431,6432],{},[1217,6433,6434,6436],{},[1156,6435,1332],{},[1145,6437,6438,6440],{},[1156,6439,1110],{},[1156,6441,1234],{},[1172,6443,1359],{"encoding":1174},[1127,6445,6446,6447,6460,6461,6474,6475,6460,6490,6503,6504,6517,6518,6531,6532,6534],{},"Zaměnit diagram ",[1115,6448,6450],{"className":6449},[1136],[1138,6451,6452],{"xmlns":1140},[1142,6453,6454,6458],{},[1145,6455,6456],{},[1156,6457,1262],{},[1172,6459,1262],{"encoding":1174}," s diagramem ",[1115,6462,6464],{"className":6463},[1136],[1138,6465,6466],{"xmlns":1140},[1142,6467,6468,6472],{},[1145,6469,6470],{},[1156,6471,1277],{},[1172,6473,1277],{"encoding":1174}," nebo diagram ",[1115,6476,6478],{"className":6477},[1136],[1138,6479,6480],{"xmlns":1140},[1142,6481,6482,6488],{},[1145,6483,6484,6486],{},[1156,6485,1292],{},[1156,6487,1110],{},[1172,6489,1297],{"encoding":1174},[1115,6491,6493],{"className":6492},[1136],[1138,6494,6495],{"xmlns":1140},[1142,6496,6497,6501],{},[1145,6498,6499],{},[1156,6500,1110],{},[1172,6502,1110],{"encoding":1174}," — při nekonstantním rozsahu podskupin se volí ",[1115,6505,6507],{"className":6506},[1136],[1138,6508,6509],{"xmlns":1140},[1142,6510,6511,6515],{},[1145,6512,6513],{},[1156,6514,1277],{},[1172,6516,1277],{"encoding":1174},", resp. ",[1115,6519,6521],{"className":6520},[1136],[1138,6522,6523],{"xmlns":1140},[1142,6524,6525,6529],{},[1145,6526,6527],{},[1156,6528,1110],{},[1172,6530,1110],{"encoding":1174},", a do ",[1434,6533,4447],{}," se zadává vektor rozsahů.",[1127,6536,6537,6538,6555,6556,6569,6570,6583,6584,1247],{},"Posuzovat diagram ",[1115,6539,6541],{"className":6540},[1136],[1138,6542,6543],{"xmlns":1140},[1142,6544,6545,6553],{},[1145,6546,6547],{},[1153,6548,6549,6551],{"accent":1121},[1156,6550,1158],{},[1148,6552,1161],{},[1172,6554,2136],{"encoding":1174}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,6557,6559],{"className":6558},[1136],[1138,6560,6561],{"xmlns":1140},[1142,6562,6563,6567],{},[1145,6564,6565],{},[1156,6566,1167],{},[1172,6568,1167],{"encoding":1174}," (resp. ",[1115,6571,6573],{"className":6572},[1136],[1138,6574,6575],{"xmlns":1140},[1142,6576,6577,6581],{},[1145,6578,6579],{},[1156,6580,1198],{},[1172,6582,1198],{"encoding":1174},"), potom diagram ",[1115,6585,6587],{"className":6586},[1136],[1138,6588,6589],{"xmlns":1140},[1142,6590,6591,6599],{},[1145,6592,6593],{},[1153,6594,6595,6597],{"accent":1121},[1156,6596,1158],{},[1148,6598,1161],{},[1172,6600,2136],{"encoding":1174},[1127,6602,6603],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1437,6605,6607],{"id":6606},"související-stránky","Související stránky",[1124,6609,6610,6619,6626,6634,6641,6649,6656],{},[1127,6611,6612],{},[6613,6614,6618],"a",{"className":6615,"dataFsResolvedFilePath":6616,"href":6617},[1531],"courses\u002Fmask.md","\u002Fwiki\u002Fmask","Metody aplikované statistiky",[1127,6620,6621],{},[6613,6622,886],{"className":6623,"dataFsResolvedFilePath":6624,"href":6625},[1531],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika",[1127,6627,6628],{},[6613,6629,6633],{"className":6630,"dataFsResolvedFilePath":6631,"href":6632},[1531],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","nahodne-veliciny-a-rozdeleni",[1127,6635,6636],{},[6613,6637,141],{"className":6638,"dataFsResolvedFilePath":6639,"href":6640},[1531],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez",[1127,6642,6643],{},[6613,6644,6648],{"className":6645,"dataFsResolvedFilePath":6646,"href":6647},[1531],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","regresni-a-korelacni-analyza",[1127,6650,6651],{},[6613,6652,716],{"className":6653,"dataFsResolvedFilePath":6654,"href":6655},[1531],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky",[1127,6657,6658],{},[6613,6659,6663],{"className":6660,"dataFsResolvedFilePath":6661,"href":6662},[1531],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","Tahák pro R",[1437,6665,6666],{"id":934},"Reference",[1110,6668,6669,6670,6674],{},"KROPÁČ, J. ",[6671,6672,6673],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[1110,6676,6677,6678,6681],{},"MONTGOMERY, D. C. ",[6671,6679,6680],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,6683,6684,6685,6688],{},"ČSN ISO 8258. ",[6671,6686,6687],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,6690,6691,6692,6695],{},"KUPKA, K. ",[6671,6693,6694],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[6697,6698,6699],"style",{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: 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pp",{"id":4793,"depth":27,"text":4794,"children":6723},[6724,6726,6728,6730,6731],{"id":4839,"depth":148,"text":6725},"CpC_p — index způsobilosti",{"id":5171,"depth":148,"text":6727},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":5367,"depth":148,"text":6729},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":5628,"depth":148,"text":5629},{"id":5820,"depth":148,"text":5821},{"id":6377,"depth":27,"text":6378},{"id":6606,"depth":27,"text":6607},{"id":934,"depth":27,"text":6666},null,"2026-10-02","md",{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":1094,"description":3265},[6742,6743,6744,6745],"raw\u002Fmask\u002F06 regulační diagramy.pdf","raw\u002Fmask\u002F07 indexy způsobilosti.pdf","raw\u002Fmask\u002Fnávod 06 a 07.pdf","raw\u002Fmask\u002Fpříklady 06 a 07.pdf","topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",[23,137,274,360,67,71],"topic","bwtPTtx6g53SO_ovQdrK_C3d6vq9rKG9Vb8jM13_yag","topics",[6752,11821,16263,21010,25702,30701],{"id":6753,"title":6754,"body":6755,"course":23,"courses":6735,"created":6736,"description":3265,"extension":6737,"meta":11812,"navigation":4236,"path":11813,"seo":11814,"sources":11815,"stem":11818,"tags":11819,"type":6748,"updated":6736,"__hash__":11820},"topics\u002Ftopics\u002Fkontingencni-tabulky.md","Kontingenční tabulky",{"type":1096,"value":6756,"toc":11802},[6757,6760,6935,6939,6955,6973,7176,7311,7904,7921,8031,8035,8066,8071,8668,8674,8887,9097,9103,9182,9293,9445,9451,9531,9552,9559,9593,9600,9603,9609,9671,9730,9877,9883,9890,9968,9971,10027,10365,10386,10490,10599,10602,10623,10626,10880,10961,10968,10972,11202,11216,11364,11498,11504,11562,11564,11583,11598,11604,11649,11668,11683,11689,11748,11750,11793,11795,11799],[1099,6758,6754],{"id":6759},"kontingenční-tabulky",[1103,6761,6763,6769],{"className":6762,"dataCallout":1108},[1106,1107],[1110,6764,6766,1122],{"className":6765},[1113],[1115,6767],{"className":6768,"ariaHidden":1121},[1118,1119,1120],[1124,6770,6771,6778,6839,6860,6899,6924],{},[1127,6772,6773,6774,6777],{},"Kontingenční tabulka zaznamenává ",[1445,6775,6776],{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1127,6779,6780,6783,6784,6803,6804,6823,6824,6838],{},[1445,6781,6782],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,6785,6787],{"className":6786},[1136],[1138,6788,6789],{"xmlns":1140},[1142,6790,6791,6800],{},[1145,6792,6793],{},[1217,6794,6795,6798],{},[1156,6796,6797],{},"H",[1919,6799,2780],{},[1172,6801,6802],{"encoding":1174},"H_0"," pomocí statistiky ",[1115,6805,6807],{"className":6806},[1136],[1138,6808,6809],{"xmlns":1140},[1142,6810,6811,6820],{},[1145,6812,6813],{},[5465,6814,6815,6818],{},[1156,6816,6817],{},"χ",[1919,6819,2302],{},[1172,6821,6822],{"encoding":1174},"\\chi^2","; rozhoduje kritický obor ",[1115,6825,6827],{"className":6826},[1136],[1138,6828,6829],{"xmlns":1140},[1142,6830,6831,6836],{},[1145,6832,6833],{},[1156,6834,6835],{},"W",[1172,6837,6835],{"encoding":1174},", prakticky p-hodnota.",[1127,6840,6841,6842,6859],{},"Aproximace ",[1115,6843,6845],{"className":6844},[1136],[1138,6846,6847],{"xmlns":1140},[1142,6848,6849,6857],{},[1145,6850,6851],{},[5465,6852,6853,6855],{},[1156,6854,6817],{},[1919,6856,2302],{},[1172,6858,6822],{"encoding":1174}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1127,6861,6862,6863,6880,6881,6884,6885,1247],{},"Zamítnutí ",[1115,6864,6866],{"className":6865},[1136],[1138,6867,6868],{"xmlns":1140},[1142,6869,6870,6878],{},[1145,6871,6872],{},[1217,6873,6874,6876],{},[1156,6875,6797],{},[1919,6877,2780],{},[1172,6879,6802],{"encoding":1174}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1445,6882,6883],{},"Cramérův koeficient kontingence"," ",[1115,6886,6888],{"className":6887},[1136],[1138,6889,6890],{"xmlns":1140},[1142,6891,6892,6897],{},[1145,6893,6894],{},[1156,6895,6896],{},"V",[1172,6898,6896],{"encoding":1174},[1127,6900,6901,6904,6905,1247],{},[1445,6902,6903],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,6906,6908],{"className":6907},[1136],[1138,6909,6910],{"xmlns":1140},[1142,6911,6912,6921],{},[1145,6913,6914,6916,6918],{},[1156,6915,1292],{},[1148,6917,5755],{},[1919,6919,6920],{},"40",[1172,6922,6923],{"encoding":1174},"n>40",[1127,6925,6926,6927,6930,6931,6934],{},"Pro ",[1445,6928,6929],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1445,6932,6933],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1437,6936,6938],{"id":6937},"kontingenční-tabulka","Kontingenční tabulka",[1110,6940,6941,6942,6945,6946,6950,6951,6954],{},"V rámci ",[6613,6943,6618],{"className":6944,"dataFsResolvedFilePath":6616,"href":6617},[1531]," navazují kontingenční tabulky na\n",[6613,6947,6949],{"className":6948,"dataFsResolvedFilePath":6639,"href":6640},[1531],"testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1445,6952,6953],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,6956,6957,6958,6961,6962,6964,6965,6968,6969,6972],{},"Znak je ",[1445,6959,6960],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1445,6963,6953],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1445,6966,6967],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1445,6970,6971],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,6974,6975,6976,6989,6990,7004,7005,7035,7036,7050,7051,7081,7082,7085,7086,7108,7109,6884,7112,7134,7135,7153,7154,7172,7173,2529],{},"Mějme ",[1115,6977,6979],{"className":6978},[1136],[1138,6980,6981],{"xmlns":1140},[1142,6982,6983,6987],{},[1145,6984,6985],{},[1156,6986,1292],{},[1172,6988,1292],{"encoding":1174}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,6991,6993],{"className":6992},[1136],[1138,6994,6995],{"xmlns":1140},[1142,6996,6997,7002],{},[1145,6998,6999],{},[1156,7000,7001],{},"A",[1172,7003,7001],{"encoding":1174}," (varianty ",[1115,7006,7008],{"className":7007},[1136],[1138,7009,7010],{"xmlns":1140},[1142,7011,7012,7032],{},[1145,7013,7014,7020,7022,7024,7026],{},[1217,7015,7016,7018],{},[1156,7017,7001],{},[1919,7019,1921],{},[1148,7021,1164],{"separator":1121},[1148,7023,2043],{},[1148,7025,1164],{"separator":1121},[1217,7027,7028,7030],{},[1156,7029,7001],{},[1156,7031,71],{},[1172,7033,7034],{"encoding":1174},"A_1,\\dots,A_r",") a ",[1115,7037,7039],{"className":7038},[1136],[1138,7040,7041],{"xmlns":1140},[1142,7042,7043,7048],{},[1145,7044,7045],{},[1156,7046,7047],{},"B",[1172,7049,7047],{"encoding":1174},"\n(varianty ",[1115,7052,7054],{"className":7053},[1136],[1138,7055,7056],{"xmlns":1140},[1142,7057,7058,7078],{},[1145,7059,7060,7066,7068,7070,7072],{},[1217,7061,7062,7064],{},[1156,7063,7047],{},[1919,7065,1921],{},[1148,7067,1164],{"separator":1121},[1148,7069,2043],{},[1148,7071,1164],{"separator":1121},[1217,7073,7074,7076],{},[1156,7075,7047],{},[1156,7077,1198],{},[1172,7079,7080],{"encoding":1174},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1445,7083,7084],{},"kontingenční tabulky",": v políčku ",[1115,7087,7089],{"className":7088},[1136],[1138,7090,7091],{"xmlns":1140},[1142,7092,7093,7105],{},[1145,7094,7095,7097,7099,7101,7103],{},[1148,7096,1151],{"stretchy":1150},[1156,7098,1223],{},[1148,7100,1164],{"separator":1121},[1156,7102,1934],{},[1148,7104,1170],{"stretchy":1150},[1172,7106,7107],{"encoding":1174},"(i,j)"," je ",[1445,7110,7111],{},"simultánní\nčetnost",[1115,7113,7115],{"className":7114},[1136],[1138,7116,7117],{"xmlns":1140},[1142,7118,7119,7131],{},[1145,7120,7121],{},[1217,7122,7123,7125],{},[1156,7124,1292],{},[1145,7126,7127,7129],{},[1156,7128,1223],{},[1156,7130,1934],{},[1172,7132,7133],{"encoding":1174},"n_{ij}",", tedy počet pokusů s variantou ",[1115,7136,7138],{"className":7137},[1136],[1138,7139,7140],{"xmlns":1140},[1142,7141,7142,7150],{},[1145,7143,7144],{},[1217,7145,7146,7148],{},[1156,7147,7001],{},[1156,7149,1223],{},[1172,7151,7152],{"encoding":1174},"A_i"," zároveň s variantou ",[1115,7155,7157],{"className":7156},[1136],[1138,7158,7159],{"xmlns":1140},[1142,7160,7161,7169],{},[1145,7162,7163],{},[1217,7164,7165,7167],{},[1156,7166,7047],{},[1156,7168,1934],{},[1172,7170,7171],{"encoding":1174},"B_j",". Řádkové a sloupcové součty\njsou ",[1445,7174,7175],{},"marginální četnosti",[1115,7177,7179],{"className":7178},[1136],[1138,7180,7181],{"xmlns":1140,"display":1897},[1142,7182,7183,7308],{},[1145,7184,7185,7196,7198,7212,7222,7224,7226,7236,7238,7252,7262,7264,7266,7268,7270,7284,7298],{},[1217,7186,7187,7189],{},[1156,7188,1292],{},[1145,7190,7191,7193],{},[1156,7192,1223],{},[1148,7194,7195],{},"∙",[1148,7197,1914],{},[1925,7199,7200,7202,7210],{},[1148,7201,1929],{},[1145,7203,7204,7206,7208],{},[1156,7205,1934],{},[1148,7207,1914],{},[1919,7209,1921],{},[1156,7211,1198],{},[1217,7213,7214,7216],{},[1156,7215,1292],{},[1145,7217,7218,7220],{},[1156,7219,1223],{},[1156,7221,1934],{},[1148,7223,1164],{"separator":1121},[1954,7225],{"width":1956},[1217,7227,7228,7230],{},[1156,7229,1292],{},[1145,7231,7232,7234],{},[1148,7233,7195],{},[1156,7235,1934],{},[1148,7237,1914],{},[1925,7239,7240,7242,7250],{},[1148,7241,1929],{},[1145,7243,7244,7246,7248],{},[1156,7245,1223],{},[1148,7247,1914],{},[1919,7249,1921],{},[1156,7251,71],{},[1217,7253,7254,7256],{},[1156,7255,1292],{},[1145,7257,7258,7260],{},[1156,7259,1223],{},[1156,7261,1934],{},[1148,7263,1164],{"separator":1121},[1954,7265],{"width":1956},[1156,7267,1292],{},[1148,7269,1914],{},[1925,7271,7272,7274,7282],{},[1148,7273,1929],{},[1145,7275,7276,7278,7280],{},[1156,7277,1223],{},[1148,7279,1914],{},[1919,7281,1921],{},[1156,7283,71],{},[1925,7285,7286,7288,7296],{},[1148,7287,1929],{},[1145,7289,7290,7292,7294],{},[1156,7291,1934],{},[1148,7293,1914],{},[1919,7295,1921],{},[1156,7297,1198],{},[1217,7299,7300,7302],{},[1156,7301,1292],{},[1145,7303,7304,7306],{},[1156,7305,1223],{},[1156,7307,1934],{},[1172,7309,7310],{"encoding":1174},"n_{i\\bullet} = \\sum_{j=1}^{s} n_{ij}, \\qquad n_{\\bullet j} = \\sum_{i=1}^{r} n_{ij}, \\qquad n = \\sum_{i=1}^r\\sum_{j=1}^s n_{ij}",[1459,7312,7313,7424],{},[1462,7314,7315],{},[1465,7316,7317,7338,7358,7378,7380,7400],{},[1468,7318,7319],{},[1115,7320,7322],{"className":7321},[1136],[1138,7323,7324],{"xmlns":1140},[1142,7325,7326,7335],{},[1145,7327,7328,7330,7333],{},[1156,7329,7001],{},[1156,7331,7332],{"mathvariant":2014},"\\",[1156,7334,7047],{},[1172,7336,7337],{"encoding":1174},"A \\backslash B",[1468,7339,7340],{},[1115,7341,7343],{"className":7342},[1136],[1138,7344,7345],{"xmlns":1140},[1142,7346,7347,7355],{},[1145,7348,7349],{},[1217,7350,7351,7353],{},[1156,7352,7047],{},[1919,7354,1921],{},[1172,7356,7357],{"encoding":1174},"B_1",[1468,7359,7360],{},[1115,7361,7363],{"className":7362},[1136],[1138,7364,7365],{"xmlns":1140},[1142,7366,7367,7375],{},[1145,7368,7369],{},[1217,7370,7371,7373],{},[1156,7372,7047],{},[1919,7374,2302],{},[1172,7376,7377],{"encoding":1174},"B_2",[1468,7379,2043],{},[1468,7381,7382],{},[1115,7383,7385],{"className":7384},[1136],[1138,7386,7387],{"xmlns":1140},[1142,7388,7389,7397],{},[1145,7390,7391],{},[1217,7392,7393,7395],{},[1156,7394,7047],{},[1156,7396,1198],{},[1172,7398,7399],{"encoding":1174},"B_s",[1468,7401,7402],{},[1115,7403,7405],{"className":7404},[1136],[1138,7406,7407],{"xmlns":1140},[1142,7408,7409,7421],{},[1145,7410,7411],{},[1217,7412,7413,7415],{},[1156,7414,1292],{},[1145,7416,7417,7419],{},[1156,7418,1223],{},[1148,7420,7195],{},[1172,7422,7423],{"encoding":1174},"n_{i\\bullet}",[1477,7425,7426,7539,7653,7669,7789],{},[1465,7427,7428,7448,7468,7489,7491,7515],{},[1482,7429,7430],{},[1115,7431,7433],{"className":7432},[1136],[1138,7434,7435],{"xmlns":1140},[1142,7436,7437,7445],{},[1145,7438,7439],{},[1217,7440,7441,7443],{},[1156,7442,7001],{},[1919,7444,1921],{},[1172,7446,7447],{"encoding":1174},"A_1",[1482,7449,7450],{},[1115,7451,7453],{"className":7452},[1136],[1138,7454,7455],{"xmlns":1140},[1142,7456,7457,7465],{},[1145,7458,7459],{},[1217,7460,7461,7463],{},[1156,7462,1292],{},[1919,7464,2644],{},[1172,7466,7467],{"encoding":1174},"n_{11}",[1482,7469,7470],{},[1115,7471,7473],{"className":7472},[1136],[1138,7474,7475],{"xmlns":1140},[1142,7476,7477,7486],{},[1145,7478,7479],{},[1217,7480,7481,7483],{},[1156,7482,1292],{},[1919,7484,7485],{},"12",[1172,7487,7488],{"encoding":1174},"n_{12}",[1482,7490,2043],{},[1482,7492,7493],{},[1115,7494,7496],{"className":7495},[1136],[1138,7497,7498],{"xmlns":1140},[1142,7499,7500,7512],{},[1145,7501,7502],{},[1217,7503,7504,7506],{},[1156,7505,1292],{},[1145,7507,7508,7510],{},[1919,7509,1921],{},[1156,7511,1198],{},[1172,7513,7514],{"encoding":1174},"n_{1s}",[1482,7516,7517],{},[1115,7518,7520],{"className":7519},[1136],[1138,7521,7522],{"xmlns":1140},[1142,7523,7524,7536],{},[1145,7525,7526],{},[1217,7527,7528,7530],{},[1156,7529,1292],{},[1145,7531,7532,7534],{},[1919,7533,1921],{},[1148,7535,7195],{},[1172,7537,7538],{"encoding":1174},"n_{1\\bullet}",[1465,7540,7541,7561,7582,7603,7605,7629],{},[1482,7542,7543],{},[1115,7544,7546],{"className":7545},[1136],[1138,7547,7548],{"xmlns":1140},[1142,7549,7550,7558],{},[1145,7551,7552],{},[1217,7553,7554,7556],{},[1156,7555,7001],{},[1919,7557,2302],{},[1172,7559,7560],{"encoding":1174},"A_2",[1482,7562,7563],{},[1115,7564,7566],{"className":7565},[1136],[1138,7567,7568],{"xmlns":1140},[1142,7569,7570,7579],{},[1145,7571,7572],{},[1217,7573,7574,7576],{},[1156,7575,1292],{},[1919,7577,7578],{},"21",[1172,7580,7581],{"encoding":1174},"n_{21}",[1482,7583,7584],{},[1115,7585,7587],{"className":7586},[1136],[1138,7588,7589],{"xmlns":1140},[1142,7590,7591,7600],{},[1145,7592,7593],{},[1217,7594,7595,7597],{},[1156,7596,1292],{},[1919,7598,7599],{},"22",[1172,7601,7602],{"encoding":1174},"n_{22}",[1482,7604,2043],{},[1482,7606,7607],{},[1115,7608,7610],{"className":7609},[1136],[1138,7611,7612],{"xmlns":1140},[1142,7613,7614,7626],{},[1145,7615,7616],{},[1217,7617,7618,7620],{},[1156,7619,1292],{},[1145,7621,7622,7624],{},[1919,7623,2302],{},[1156,7625,1198],{},[1172,7627,7628],{"encoding":1174},"n_{2s}",[1482,7630,7631],{},[1115,7632,7634],{"className":7633},[1136],[1138,7635,7636],{"xmlns":1140},[1142,7637,7638,7650],{},[1145,7639,7640],{},[1217,7641,7642,7644],{},[1156,7643,1292],{},[1145,7645,7646,7648],{},[1919,7647,2302],{},[1148,7649,7195],{},[1172,7651,7652],{"encoding":1174},"n_{2\\bullet}",[1465,7654,7655,7658,7660,7662,7665,7667],{},[1482,7656,7657],{},"⋮",[1482,7659,7657],{},[1482,7661,7657],{},[1482,7663,7664],{},"⋱",[1482,7666,7657],{},[1482,7668,7657],{},[1465,7670,7671,7691,7715,7739,7741,7765],{},[1482,7672,7673],{},[1115,7674,7676],{"className":7675},[1136],[1138,7677,7678],{"xmlns":1140},[1142,7679,7680,7688],{},[1145,7681,7682],{},[1217,7683,7684,7686],{},[1156,7685,7001],{},[1156,7687,71],{},[1172,7689,7690],{"encoding":1174},"A_r",[1482,7692,7693],{},[1115,7694,7696],{"className":7695},[1136],[1138,7697,7698],{"xmlns":1140},[1142,7699,7700,7712],{},[1145,7701,7702],{},[1217,7703,7704,7706],{},[1156,7705,1292],{},[1145,7707,7708,7710],{},[1156,7709,71],{},[1919,7711,1921],{},[1172,7713,7714],{"encoding":1174},"n_{r1}",[1482,7716,7717],{},[1115,7718,7720],{"className":7719},[1136],[1138,7721,7722],{"xmlns":1140},[1142,7723,7724,7736],{},[1145,7725,7726],{},[1217,7727,7728,7730],{},[1156,7729,1292],{},[1145,7731,7732,7734],{},[1156,7733,71],{},[1919,7735,2302],{},[1172,7737,7738],{"encoding":1174},"n_{r2}",[1482,7740,2043],{},[1482,7742,7743],{},[1115,7744,7746],{"className":7745},[1136],[1138,7747,7748],{"xmlns":1140},[1142,7749,7750,7762],{},[1145,7751,7752],{},[1217,7753,7754,7756],{},[1156,7755,1292],{},[1145,7757,7758,7760],{},[1156,7759,71],{},[1156,7761,1198],{},[1172,7763,7764],{"encoding":1174},"n_{rs}",[1482,7766,7767],{},[1115,7768,7770],{"className":7769},[1136],[1138,7771,7772],{"xmlns":1140},[1142,7773,7774,7786],{},[1145,7775,7776],{},[1217,7777,7778,7780],{},[1156,7779,1292],{},[1145,7781,7782,7784],{},[1156,7783,71],{},[1148,7785,7195],{},[1172,7787,7788],{"encoding":1174},"n_{r\\bullet}",[1465,7790,7791,7815,7839,7863,7865,7889],{},[1482,7792,7793],{},[1115,7794,7796],{"className":7795},[1136],[1138,7797,7798],{"xmlns":1140},[1142,7799,7800,7812],{},[1145,7801,7802],{},[1217,7803,7804,7806],{},[1156,7805,1292],{},[1145,7807,7808,7810],{},[1148,7809,7195],{},[1156,7811,1934],{},[1172,7813,7814],{"encoding":1174},"n_{\\bullet j}",[1482,7816,7817],{},[1115,7818,7820],{"className":7819},[1136],[1138,7821,7822],{"xmlns":1140},[1142,7823,7824,7836],{},[1145,7825,7826],{},[1217,7827,7828,7830],{},[1156,7829,1292],{},[1145,7831,7832,7834],{},[1148,7833,7195],{},[1919,7835,1921],{},[1172,7837,7838],{"encoding":1174},"n_{\\bullet 1}",[1482,7840,7841],{},[1115,7842,7844],{"className":7843},[1136],[1138,7845,7846],{"xmlns":1140},[1142,7847,7848,7860],{},[1145,7849,7850],{},[1217,7851,7852,7854],{},[1156,7853,1292],{},[1145,7855,7856,7858],{},[1148,7857,7195],{},[1919,7859,2302],{},[1172,7861,7862],{"encoding":1174},"n_{\\bullet 2}",[1482,7864,2043],{},[1482,7866,7867],{},[1115,7868,7870],{"className":7869},[1136],[1138,7871,7872],{"xmlns":1140},[1142,7873,7874,7886],{},[1145,7875,7876],{},[1217,7877,7878,7880],{},[1156,7879,1292],{},[1145,7881,7882,7884],{},[1148,7883,7195],{},[1156,7885,1198],{},[1172,7887,7888],{"encoding":1174},"n_{\\bullet s}",[1482,7890,7891],{},[1115,7892,7894],{"className":7893},[1136],[1138,7895,7896],{"xmlns":1140},[1142,7897,7898,7902],{},[1145,7899,7900],{},[1156,7901,1292],{},[1172,7903,1292],{"encoding":1174},[1110,7905,7906,7907,7920],{},"Vydělením četností počtem opakování ",[1115,7908,7910],{"className":7909},[1136],[1138,7911,7912],{"xmlns":1140},[1142,7913,7914,7918],{},[1145,7915,7916],{},[1156,7917,1292],{},[1172,7919,1292],{"encoding":1174}," dostaneme odhady pravděpodobností:",[1115,7922,7924],{"className":7923},[1136],[1138,7925,7926],{"xmlns":1140,"display":1897},[1142,7927,7928,8028],{},[1145,7929,7930,7944,7946,7960,7962,7964,7978,7980,7994,7996,7998,8012,8014],{},[1217,7931,7932,7938],{},[1153,7933,7934,7936],{"accent":1121},[1156,7935,1110],{},[1148,7937,6165],{},[1145,7939,7940,7942],{},[1156,7941,1223],{},[1156,7943,1934],{},[1148,7945,1914],{},[1916,7947,7948,7958],{},[1217,7949,7950,7952],{},[1156,7951,1292],{},[1145,7953,7954,7956],{},[1156,7955,1223],{},[1156,7957,1934],{},[1156,7959,1292],{},[1148,7961,1164],{"separator":1121},[1954,7963],{"width":1956},[1217,7965,7966,7972],{},[1153,7967,7968,7970],{"accent":1121},[1156,7969,1110],{},[1148,7971,6165],{},[1145,7973,7974,7976],{},[1156,7975,1223],{},[1148,7977,7195],{},[1148,7979,1914],{},[1916,7981,7982,7992],{},[1217,7983,7984,7986],{},[1156,7985,1292],{},[1145,7987,7988,7990],{},[1156,7989,1223],{},[1148,7991,7195],{},[1156,7993,1292],{},[1148,7995,1164],{"separator":1121},[1954,7997],{"width":1956},[1217,7999,8000,8006],{},[1153,8001,8002,8004],{"accent":1121},[1156,8003,1110],{},[1148,8005,6165],{},[1145,8007,8008,8010],{},[1148,8009,7195],{},[1156,8011,1934],{},[1148,8013,1914],{},[1916,8015,8016,8026],{},[1217,8017,8018,8020],{},[1156,8019,1292],{},[1145,8021,8022,8024],{},[1148,8023,7195],{},[1156,8025,1934],{},[1156,8027,1292],{},[1172,8029,8030],{"encoding":1174},"\\hat p_{ij} = \\frac{n_{ij}}{n}, \\qquad \\hat p_{i\\bullet} = \\frac{n_{i\\bullet}}{n}, \\qquad \\hat p_{\\bullet j} = \\frac{n_{\\bullet j}}{n}",[1437,8032,8034],{"id":8033},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,8036,8037,8038,8051,8052,8065],{},"Test ověřuje, zda varianty znaku ",[1115,8039,8041],{"className":8040},[1136],[1138,8042,8043],{"xmlns":1140},[1142,8044,8045,8049],{},[1145,8046,8047],{},[1156,8048,7001],{},[1172,8050,7001],{"encoding":1174}," a varianty znaku ",[1115,8053,8055],{"className":8054},[1136],[1138,8056,8057],{"xmlns":1140},[1142,8058,8059,8063],{},[1145,8060,8061],{},[1156,8062,7047],{},[1172,8064,7047],{"encoding":1174}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,8067,8068],{},[1445,8069,8070],{},"Postup testu:",[1538,8072,8073,8202,8518,8600],{},[1127,8074,8075,8129,8130,1176,8156,8182,8183,8201],{},[1115,8076,8078],{"className":8077},[1136],[1138,8079,8080],{"xmlns":1140},[1142,8081,8082,8126],{},[1145,8083,8084,8090,8092,8102,8104,8114,8116],{},[1217,8085,8086,8088],{},[1156,8087,6797],{},[1919,8089,2780],{},[1148,8091,2529],{},[1217,8093,8094,8096],{},[1156,8095,1110],{},[1145,8097,8098,8100],{},[1156,8099,1223],{},[1156,8101,1934],{},[1148,8103,1914],{},[1217,8105,8106,8108],{},[1156,8107,1110],{},[1145,8109,8110,8112],{},[1156,8111,1223],{},[1148,8113,7195],{},[5009,8115,5011],{},[1217,8117,8118,8120],{},[1156,8119,1110],{},[1145,8121,8122,8124],{},[1148,8123,7195],{},[1156,8125,1934],{},[1172,8127,8128],{"encoding":1174},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,8131,8133],{"className":8132},[1136],[1138,8134,8135],{"xmlns":1140},[1142,8136,8137,8153],{},[1145,8138,8139,8141,8143,8145,8147,8149,8151],{},[1156,8140,1223],{},[1148,8142,1914],{},[1919,8144,1921],{},[1148,8146,1164],{"separator":1121},[1148,8148,2043],{},[1148,8150,1164],{"separator":1121},[1156,8152,71],{},[1172,8154,8155],{"encoding":1174},"i = 1,\\dots,r",[1115,8157,8159],{"className":8158},[1136],[1138,8160,8161],{"xmlns":1140},[1142,8162,8163,8179],{},[1145,8164,8165,8167,8169,8171,8173,8175,8177],{},[1156,8166,1934],{},[1148,8168,1914],{},[1919,8170,1921],{},[1148,8172,1164],{"separator":1121},[1148,8174,2043],{},[1148,8176,1164],{"separator":1121},[1156,8178,1198],{},[1172,8180,8181],{"encoding":1174},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,8184,8186],{"className":8185},[1136],[1138,8187,8188],{"xmlns":1140},[1142,8189,8190,8198],{},[1145,8191,8192],{},[1217,8193,8194,8196],{},[1156,8195,6797],{},[1919,8197,1921],{},[1172,8199,8200],{"encoding":1174},"H_1",": znaky jsou závislé.",[1127,8203,8204,8205,8361,8364,8365,8382,8383,8415,8416,7108,8474,8477,8478,8499,8500,8517],{},"Testové kritérium",[1115,8206,8208],{"className":8207},[1136],[1138,8209,8210],{"xmlns":1140,"display":1897},[1142,8211,8212,8358],{},[1145,8213,8214,8220,8222,8236,8250,8308,8310,8312,8326,8328,8342,8344],{},[5465,8215,8216,8218],{},[1156,8217,6817],{},[1919,8219,2302],{},[1148,8221,1914],{},[1925,8223,8224,8226,8234],{},[1148,8225,1929],{},[1145,8227,8228,8230,8232],{},[1156,8229,1223],{},[1148,8231,1914],{},[1919,8233,1921],{},[1156,8235,71],{},[1925,8237,8238,8240,8248],{},[1148,8239,1929],{},[1145,8241,8242,8244,8246],{},[1156,8243,1934],{},[1148,8245,1914],{},[1919,8247,1921],{},[1156,8249,1198],{},[1916,8251,8252,8290],{},[1145,8253,8254,8256,8266,8268,8270,8284],{},[1148,8255,1151],{"stretchy":1150},[1217,8257,8258,8260],{},[1156,8259,1292],{},[1145,8261,8262,8264],{},[1156,8263,1223],{},[1156,8265,1934],{},[1148,8267,1990],{},[1156,8269,1292],{},[1217,8271,8272,8278],{},[1153,8273,8274,8276],{"accent":1121},[1156,8275,1110],{},[1148,8277,6165],{},[1145,8279,8280,8282],{},[1156,8281,1223],{},[1156,8283,1934],{},[5465,8285,8286,8288],{},[1148,8287,1170],{"stretchy":1150},[1919,8289,2302],{},[1145,8291,8292,8294],{},[1156,8293,1292],{},[1217,8295,8296,8302],{},[1153,8297,8298,8300],{"accent":1121},[1156,8299,1110],{},[1148,8301,6165],{},[1145,8303,8304,8306],{},[1156,8305,1223],{},[1156,8307,1934],{},[1148,8309,1164],{"separator":1121},[1954,8311],{"width":1956},[1217,8313,8314,8320],{},[1153,8315,8316,8318],{"accent":1121},[1156,8317,1110],{},[1148,8319,6165],{},[1145,8321,8322,8324],{},[1156,8323,1223],{},[1156,8325,1934],{},[1148,8327,1914],{},[1217,8329,8330,8336],{},[1153,8331,8332,8334],{"accent":1121},[1156,8333,1110],{},[1148,8335,6165],{},[1145,8337,8338,8340],{},[1156,8339,1223],{},[1148,8341,7195],{},[5009,8343,5011],{},[1217,8345,8346,8352],{},[1153,8347,8348,8350],{"accent":1121},[1156,8349,1110],{},[1148,8351,6165],{},[1145,8353,8354,8356],{},[1148,8355,7195],{},[1156,8357,1934],{},[1172,8359,8360],{"encoding":1174},"\\chi^2 = \\sum_{i=1}^{r}\\sum_{j=1}^{s} \\frac{(n_{ij} - n\\hat p_{ij})^2}{n\\hat p_{ij}}, \\qquad \\hat p_{ij} = \\hat p_{i\\bullet}\\,\\hat p_{\\bullet j}",[8362,8363],"br",{},"má asymptoticky Pearsonovo (",[1115,8366,8368],{"className":8367},[1136],[1138,8369,8370],{"xmlns":1140},[1142,8371,8372,8380],{},[1145,8373,8374],{},[5465,8375,8376,8378],{},[1156,8377,6817],{},[1919,8379,2302],{},[1172,8381,6822],{"encoding":1174},") rozdělení o ",[1115,8384,8386],{"className":8385},[1136],[1138,8387,8388],{"xmlns":1140},[1142,8389,8390,8412],{},[1145,8391,8392,8394,8396,8398,8400,8402,8404,8406,8408,8410],{},[1148,8393,1151],{"stretchy":1150},[1156,8395,71],{},[1148,8397,1990],{},[1919,8399,1921],{},[1148,8401,1170],{"stretchy":1150},[1148,8403,1151],{"stretchy":1150},[1156,8405,1198],{},[1148,8407,1990],{},[1919,8409,1921],{},[1148,8411,1170],{"stretchy":1150},[1172,8413,8414],{"encoding":1174},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,8417,8419],{"className":8418},[1136],[1138,8420,8421],{"xmlns":1140},[1142,8422,8423,8471],{},[1145,8424,8425,8427,8441,8443],{},[1156,8426,1292],{},[1217,8428,8429,8435],{},[1153,8430,8431,8433],{"accent":1121},[1156,8432,1110],{},[1148,8434,6165],{},[1145,8436,8437,8439],{},[1156,8438,1223],{},[1156,8440,1934],{},[1148,8442,1914],{},[4995,8444,8445],{"scriptlevel":2780,"displaystyle":1121},[1916,8446,8447,8469],{},[1145,8448,8449,8459],{},[1217,8450,8451,8453],{},[1156,8452,1292],{},[1145,8454,8455,8457],{},[1156,8456,1223],{},[1148,8458,7195],{},[1217,8460,8461,8463],{},[1156,8462,1292],{},[1145,8464,8465,8467],{},[1148,8466,7195],{},[1156,8468,1934],{},[1156,8470,1292],{},[1172,8472,8473],{"encoding":1174},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1445,8475,8476],{},"očekávaná četnost"," políčka ",[1115,8479,8481],{"className":8480},[1136],[1138,8482,8483],{"xmlns":1140},[1142,8484,8485,8497],{},[1145,8486,8487,8489,8491,8493,8495],{},[1148,8488,1151],{"stretchy":1150},[1156,8490,1223],{},[1148,8492,1164],{"separator":1121},[1156,8494,1934],{},[1148,8496,1170],{"stretchy":1150},[1172,8498,7107],{"encoding":1174}," — četnost, kterou bychom čekali, kdyby ",[1115,8501,8503],{"className":8502},[1136],[1138,8504,8505],{"xmlns":1140},[1142,8506,8507,8515],{},[1145,8508,8509],{},[1217,8510,8511,8513],{},[1156,8512,6797],{},[1919,8514,2780],{},[1172,8516,6802],{"encoding":1174}," platila.",[1127,8519,8520,8521,1247],{},"Kritický obor: ",[1115,8522,8524],{"className":8523},[1136],[1138,8525,8526],{"xmlns":1140},[1142,8527,8528,8597],{},[1145,8529,8530,8532,8534,8537,8543,8545,8551,8554,8570,8572,8574,8576,8578,8580,8582,8584,8586,8588,8590,8592,8594],{},[1156,8531,6835],{},[1148,8533,1914],{},[1148,8535,8536],{"stretchy":1150},"{",[5465,8538,8539,8541],{},[1156,8540,6817],{},[1919,8542,2302],{},[1148,8544,2529],{},[5465,8546,8547,8549],{},[1156,8548,6817],{},[1919,8550,2302],{},[1148,8552,8553],{},"≥",[8555,8556,8557,8559,8568],"msubsup",{},[1156,8558,6817],{},[1145,8560,8561,8563,8565],{},[1919,8562,1921],{},[1148,8564,1990],{},[1156,8566,8567],{},"α",[1919,8569,2302],{},[1148,8571,1151],{"stretchy":1150},[1148,8573,1151],{"stretchy":1150},[1156,8575,71],{},[1148,8577,1990],{},[1919,8579,1921],{},[1148,8581,1170],{"stretchy":1150},[1148,8583,1151],{"stretchy":1150},[1156,8585,1198],{},[1148,8587,1990],{},[1919,8589,1921],{},[1148,8591,1170],{"stretchy":1150},[1148,8593,1170],{"stretchy":1150},[1148,8595,8596],{"stretchy":1150},"}",[1172,8598,8599],{"encoding":1174},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1127,8601,8602,8603,8616,8617,8631,8632,8649,8650,8667],{},"Padne-li testové kritérium do ",[1115,8604,8606],{"className":8605},[1136],[1138,8607,8608],{"xmlns":1140},[1142,8609,8610,8614],{},[1145,8611,8612],{},[1156,8613,6835],{},[1172,8615,6835],{"encoding":1174},", zamítáme na hladině ",[1115,8618,8620],{"className":8619},[1136],[1138,8621,8622],{"xmlns":1140},[1142,8623,8624,8628],{},[1145,8625,8626],{},[1156,8627,8567],{},[1172,8629,8630],{"encoding":1174},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,8633,8635],{"className":8634},[1136],[1138,8636,8637],{"xmlns":1140},[1142,8638,8639,8647],{},[1145,8640,8641],{},[1217,8642,8643,8645],{},[1156,8644,6797],{},[1919,8646,1921],{},[1172,8648,8200],{"encoding":1174},"; jinak nemáme důvod ",[1115,8651,8653],{"className":8652},[1136],[1138,8654,8655],{"xmlns":1140},[1142,8656,8657,8665],{},[1145,8658,8659],{},[1217,8660,8661,8663],{},[1156,8662,6797],{},[1919,8664,2780],{},[1172,8666,6802],{"encoding":1174}," zamítnout.",[1110,8669,8670,8671,1247],{},"V R počítá test i očekávané četnosti funkce ",[1434,8672,8673],{},"chisq.test()",[1103,8675,8677,8684,8687,8690,8832],{"className":8676,"dataCallout":2145},[1106,2144],[1110,8678,8680,8683],{"className":8679},[1113],[1115,8681],{"className":8682,"ariaHidden":1121},[1118,2152,1120],"Příklad: nákup potravin na internetu a vzdělání",[1110,8685,8686],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,8688,8689],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1459,8691,8692,8731],{},[1462,8693,8694],{},[1465,8695,8696,8699,8702,8705,8708],{},[1468,8697,8698],{},"vzdělání \\ nákup",[1468,8700,8701],{},"ano",[1468,8703,8704],{},"ne, ale plánuji",[1468,8706,8707],{},"ne, neplánuji",[1468,8709,8710],{},[1115,8711,8713],{"className":8712},[1136],[1138,8714,8715],{"xmlns":1140},[1142,8716,8717,8729],{},[1145,8718,8719],{},[1217,8720,8721,8723],{},[1156,8722,1292],{},[1145,8724,8725,8727],{},[1156,8726,1223],{},[1148,8728,7195],{},[1172,8730,7423],{"encoding":1174},[1477,8732,8733,8747,8763,8780,8795],{},[1465,8734,8735,8738,8740,8742,8744],{},[1482,8736,8737],{},"SŠ bez maturity",[1482,8739,2206],{},[1482,8741,2671],{},[1482,8743,7485],{},[1482,8745,8746],{},"29",[1465,8748,8749,8752,8755,8758,8760],{},[1482,8750,8751],{},"SŠ s maturitou, VOŠ",[1482,8753,8754],{},"31",[1482,8756,8757],{},"62",[1482,8759,2413],{},[1482,8761,8762],{},"164",[1465,8764,8765,8768,8771,8774,8777],{},[1482,8766,8767],{},"VŠ",[1482,8769,8770],{},"44",[1482,8772,8773],{},"58",[1482,8775,8776],{},"66",[1482,8778,8779],{},"168",[1465,8781,8782,8785,8787,8790,8792],{},[1482,8783,8784],{},"ZŠ",[1482,8786,2327],{},[1482,8788,8789],{},"9",[1482,8791,7485],{},[1482,8793,8794],{},"24",[1465,8796,8797,8820,8823,8826,8829],{},[1482,8798,8799],{},[1115,8800,8802],{"className":8801},[1136],[1138,8803,8804],{"xmlns":1140},[1142,8805,8806,8818],{},[1145,8807,8808],{},[1217,8809,8810,8812],{},[1156,8811,1292],{},[1145,8813,8814,8816],{},[1148,8815,7195],{},[1156,8817,1934],{},[1172,8819,7814],{"encoding":1174},[1482,8821,8822],{},"82",[1482,8824,8825],{},"142",[1482,8827,8828],{},"161",[1482,8830,8831],{},"385",[1110,8833,8834,8886],{},[1115,8835,8837],{"className":8836},[1136],[1138,8838,8839],{"xmlns":1140},[1142,8840,8841,8883],{},[1145,8842,8843,8849,8851,8861,8863,8873],{},[1217,8844,8845,8847],{},[1156,8846,6797],{},[1919,8848,2780],{},[1148,8850,2529],{},[1217,8852,8853,8855],{},[1156,8854,1110],{},[1145,8856,8857,8859],{},[1156,8858,1223],{},[1156,8860,1934],{},[1148,8862,1914],{},[1217,8864,8865,8867],{},[1156,8866,1110],{},[1145,8868,8869,8871],{},[1156,8870,1223],{},[1148,8872,7195],{},[1217,8874,8875,8877],{},[1156,8876,1110],{},[1145,8878,8879,8881],{},[1148,8880,7195],{},[1156,8882,1934],{},[1172,8884,8885],{"encoding":1174},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3261,8888,8890],{"className":3263,"code":8889,"language":71,"meta":3265,"style":3265},"tab1 \u003C- matrix(c(4, 13, 12,\n                 31, 62, 71,\n                 44, 58, 66,\n                 3,  9, 12),\n               nrow = 4, byrow = TRUE,\n               dimnames = list(\n                 vzdelani = c(\"SS bez maturity\", \"SS s maturitou nebo VOS\", \"VS\", \"ZS\"),\n                 nakup    = c(\"ano\", \"ne, ale planuji\", \"ne, neplanuji\")))\nchisq.test(tab1)\nchisq.test(tab1)$expected\n",[1434,8891,8892,8923,8940,8957,8975,8995,9008,9041,9069,9081],{"__ignoreMap":3265},[1115,8893,8894,8897,8899,8902,8904,8906,8908,8910,8912,8915,8917,8920],{"class":3270,"line":10},[1115,8895,8896],{"class":3280},"tab1",[1115,8898,3291],{"class":3273},[1115,8900,8901],{"class":3294}," matrix",[1115,8903,1151],{"class":3277},[1115,8905,1262],{"class":3294},[1115,8907,1151],{"class":3277},[1115,8909,2206],{"class":3312},[1115,8911,1164],{"class":3273},[1115,8913,8914],{"class":3312}," 13",[1115,8916,1164],{"class":3273},[1115,8918,8919],{"class":3312}," 12",[1115,8921,8922],{"class":3273},",\n",[1115,8924,8925,8928,8930,8933,8935,8938],{"class":3270,"line":27},[1115,8926,8927],{"class":3312},"                 31",[1115,8929,1164],{"class":3273},[1115,8931,8932],{"class":3312}," 62",[1115,8934,1164],{"class":3273},[1115,8936,8937],{"class":3312}," 71",[1115,8939,8922],{"class":3273},[1115,8941,8942,8945,8947,8950,8952,8955],{"class":3270,"line":148},[1115,8943,8944],{"class":3312},"                 44",[1115,8946,1164],{"class":3273},[1115,8948,8949],{"class":3312}," 58",[1115,8951,1164],{"class":3273},[1115,8953,8954],{"class":3312}," 66",[1115,8956,8922],{"class":3273},[1115,8958,8959,8962,8964,8967,8969,8971,8973],{"class":3270,"line":111},[1115,8960,8961],{"class":3312},"                 3",[1115,8963,1164],{"class":3273},[1115,8965,8966],{"class":3312},"  9",[1115,8968,1164],{"class":3273},[1115,8970,8919],{"class":3312},[1115,8972,1170],{"class":3277},[1115,8974,8922],{"class":3273},[1115,8976,8977,8980,8982,8984,8986,8989,8991,8993],{"class":3270,"line":96},[1115,8978,8979],{"class":3280},"               nrow",[1115,8981,3309],{"class":3273},[1115,8983,4184],{"class":3312},[1115,8985,1164],{"class":3273},[1115,8987,8988],{"class":3280}," byrow",[1115,8990,3309],{"class":3273},[1115,8992,3313],{"class":3312},[1115,8994,8922],{"class":3273},[1115,8996,8997,9000,9002,9005],{"class":3270,"line":89},[1115,8998,8999],{"class":3280},"               dimnames",[1115,9001,3309],{"class":3273},[1115,9003,9004],{"class":3294}," list",[1115,9006,9007],{"class":3277},"(\n",[1115,9009,9010,9013,9015,9017,9019,9022,9024,9027,9029,9032,9034,9037,9039],{"class":3270,"line":82},[1115,9011,9012],{"class":3280},"                 vzdelani",[1115,9014,3309],{"class":3273},[1115,9016,4142],{"class":3294},[1115,9018,1151],{"class":3277},[1115,9020,9021],{"class":3300},"\"SS bez maturity\"",[1115,9023,1164],{"class":3273},[1115,9025,9026],{"class":3300}," \"SS s maturitou nebo VOS\"",[1115,9028,1164],{"class":3273},[1115,9030,9031],{"class":3300}," \"VS\"",[1115,9033,1164],{"class":3273},[1115,9035,9036],{"class":3300}," \"ZS\"",[1115,9038,1170],{"class":3277},[1115,9040,8922],{"class":3273},[1115,9042,9043,9046,9049,9051,9053,9056,9058,9061,9063,9066],{"class":3270,"line":75},[1115,9044,9045],{"class":3280},"                 nakup",[1115,9047,9048],{"class":3273},"    =",[1115,9050,4142],{"class":3294},[1115,9052,1151],{"class":3277},[1115,9054,9055],{"class":3300},"\"ano\"",[1115,9057,1164],{"class":3273},[1115,9059,9060],{"class":3300}," \"ne, ale planuji\"",[1115,9062,1164],{"class":3273},[1115,9064,9065],{"class":3300}," \"ne, neplanuji\"",[1115,9067,9068],{"class":3277},")))\n",[1115,9070,9072,9075,9077,9079],{"class":3270,"line":9071},9,[1115,9073,9074],{"class":3294},"chisq.test",[1115,9076,1151],{"class":3277},[1115,9078,8896],{"class":3280},[1115,9080,3283],{"class":3277},[1115,9082,9083,9085,9087,9089,9091,9094],{"class":3270,"line":72},[1115,9084,9074],{"class":3294},[1115,9086,1151],{"class":3277},[1115,9088,8896],{"class":3280},[1115,9090,1170],{"class":3277},[1115,9092,9093],{"class":3273},"$",[1115,9095,9096],{"class":3280},"expected\n",[3261,9098,9101],{"className":9099,"code":9100,"language":4279,"meta":3265},[4277],"    Pearson's Chi-squared test\n\ndata:  tab1\nX-squared = 5.4875, df = 6, p-value = 0.483\n\n                         nakup\nvzdelani                        ano ne, ale planuji ne, neplanuji\n  SS bez maturity          6.176623       10.696104      12.12727\n  SS s maturitou nebo VOS 34.929870       60.488312      68.58182\n  VS                      35.781818       61.963636      70.25455\n  ZS                       5.111688        8.851948      10.03636\n",[1434,9102,9100],{"__ignoreMap":3265},[1110,9104,9105,9106,9129,9130,9143,9144,4984,9164,9181],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,9107,9109],{"className":9108},[1136],[1138,9110,9111],{"xmlns":1140},[1142,9112,9113,9126],{},[1145,9114,9115,9121,9123],{},[5465,9116,9117,9119],{},[1156,9118,6817],{},[1919,9120,2302],{},[1148,9122,1914],{},[1919,9124,9125],{},"5,49",[1172,9127,9128],{"encoding":1174},"\\chi^2 = 5{,}49"," s ",[1115,9131,9133],{"className":9132},[1136],[1138,9134,9135],{"xmlns":1140},[1142,9136,9137,9141],{},[1145,9138,9139],{},[1919,9140,2437],{},[1172,9142,2437],{"encoding":1174}," stupni\nvolnosti dává p-hodnotu ",[1115,9145,9147],{"className":9146},[1136],[1138,9148,9149],{"xmlns":1140},[1142,9150,9151,9161],{},[1145,9152,9153,9156,9158],{},[1919,9154,9155],{},"0,483",[1148,9157,5755],{},[1919,9159,9160],{},"0,05",[1172,9162,9163],{"encoding":1174},"0{,}483 > 0{,}05",[1115,9165,9167],{"className":9166},[1136],[1138,9168,9169],{"xmlns":1140},[1142,9170,9171,9179],{},[1145,9172,9173],{},[1217,9174,9175,9177],{},[1156,9176,6797],{},[1919,9178,2780],{},[1172,9180,6802],{"encoding":1174}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,9183,9185,9192,9195,9239],{"className":9184,"dataCallout":2145},[1106,2144],[1110,9186,9188,9191],{"className":9187},[1113],[1115,9189],{"className":9190,"ariaHidden":1121},[1118,2152,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,9193,9194],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1459,9196,9197,9211],{},[1462,9198,9199],{},[1465,9200,9201,9204,9207,9209],{},[1468,9202,9203],{},"zveřejňuje \\ vzdělání",[1468,9205,9206],{},"SŠ",[1468,9208,8767],{},[1468,9210,8784],{},[1477,9212,9213,9226],{},[1465,9214,9215,9218,9220,9223],{},[1482,9216,9217],{},"ne",[1482,9219,2187],{},[1482,9221,9222],{},"33",[1482,9224,9225],{},"39",[1465,9227,9228,9230,9233,9236],{},[1482,9229,8701],{},[1482,9231,9232],{},"25",[1482,9234,9235],{},"28",[1482,9237,9238],{},"76",[1110,9240,9241,9292],{},[1115,9242,9244],{"className":9243},[1136],[1138,9245,9246],{"xmlns":1140},[1142,9247,9248,9290],{},[1145,9249,9250,9256,9258,9268,9270,9280],{},[1217,9251,9252,9254],{},[1156,9253,6797],{},[1919,9255,2780],{},[1148,9257,2529],{},[1217,9259,9260,9262],{},[1156,9261,1110],{},[1145,9263,9264,9266],{},[1156,9265,1223],{},[1156,9267,1934],{},[1148,9269,1914],{},[1217,9271,9272,9274],{},[1156,9273,1110],{},[1145,9275,9276,9278],{},[1156,9277,1223],{},[1148,9279,7195],{},[1217,9281,9282,9284],{},[1156,9283,1110],{},[1145,9285,9286,9288],{},[1148,9287,7195],{},[1156,9289,1934],{},[1172,9291,8885],{"encoding":1174}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3261,9294,9296],{"className":3263,"code":9295,"language":71,"meta":3265,"style":3265},"tab2 \u003C- matrix(c(20, 33, 39,\n                 25, 28, 76),\n               nrow = 2, byrow = TRUE,\n               dimnames = list(\n                 zverejnuje = c(\"ne\", \"ano\"),\n                 vzdelani   = c(\"SS\", \"VS\", \"ZS\")))\nchisq.test(tab2)\nchisq.test(tab2)$expected\n",[1434,9297,9298,9327,9346,9364,9374,9397,9421,9431],{"__ignoreMap":3265},[1115,9299,9300,9303,9305,9307,9309,9311,9313,9315,9317,9320,9322,9325],{"class":3270,"line":10},[1115,9301,9302],{"class":3280},"tab2",[1115,9304,3291],{"class":3273},[1115,9306,8901],{"class":3294},[1115,9308,1151],{"class":3277},[1115,9310,1262],{"class":3294},[1115,9312,1151],{"class":3277},[1115,9314,2187],{"class":3312},[1115,9316,1164],{"class":3273},[1115,9318,9319],{"class":3312}," 33",[1115,9321,1164],{"class":3273},[1115,9323,9324],{"class":3312}," 39",[1115,9326,8922],{"class":3273},[1115,9328,9329,9332,9334,9337,9339,9342,9344],{"class":3270,"line":27},[1115,9330,9331],{"class":3312},"                 25",[1115,9333,1164],{"class":3273},[1115,9335,9336],{"class":3312}," 28",[1115,9338,1164],{"class":3273},[1115,9340,9341],{"class":3312}," 76",[1115,9343,1170],{"class":3277},[1115,9345,8922],{"class":3273},[1115,9347,9348,9350,9352,9354,9356,9358,9360,9362],{"class":3270,"line":148},[1115,9349,8979],{"class":3280},[1115,9351,3309],{"class":3273},[1115,9353,4156],{"class":3312},[1115,9355,1164],{"class":3273},[1115,9357,8988],{"class":3280},[1115,9359,3309],{"class":3273},[1115,9361,3313],{"class":3312},[1115,9363,8922],{"class":3273},[1115,9365,9366,9368,9370,9372],{"class":3270,"line":111},[1115,9367,8999],{"class":3280},[1115,9369,3309],{"class":3273},[1115,9371,9004],{"class":3294},[1115,9373,9007],{"class":3277},[1115,9375,9376,9379,9381,9383,9385,9388,9390,9393,9395],{"class":3270,"line":96},[1115,9377,9378],{"class":3280},"                 zverejnuje",[1115,9380,3309],{"class":3273},[1115,9382,4142],{"class":3294},[1115,9384,1151],{"class":3277},[1115,9386,9387],{"class":3300},"\"ne\"",[1115,9389,1164],{"class":3273},[1115,9391,9392],{"class":3300}," \"ano\"",[1115,9394,1170],{"class":3277},[1115,9396,8922],{"class":3273},[1115,9398,9399,9401,9404,9406,9408,9411,9413,9415,9417,9419],{"class":3270,"line":89},[1115,9400,9012],{"class":3280},[1115,9402,9403],{"class":3273},"   =",[1115,9405,4142],{"class":3294},[1115,9407,1151],{"class":3277},[1115,9409,9410],{"class":3300},"\"SS\"",[1115,9412,1164],{"class":3273},[1115,9414,9031],{"class":3300},[1115,9416,1164],{"class":3273},[1115,9418,9036],{"class":3300},[1115,9420,9068],{"class":3277},[1115,9422,9423,9425,9427,9429],{"class":3270,"line":82},[1115,9424,9074],{"class":3294},[1115,9426,1151],{"class":3277},[1115,9428,9302],{"class":3280},[1115,9430,3283],{"class":3277},[1115,9432,9433,9435,9437,9439,9441,9443],{"class":3270,"line":75},[1115,9434,9074],{"class":3294},[1115,9436,1151],{"class":3277},[1115,9438,9302],{"class":3280},[1115,9440,1170],{"class":3277},[1115,9442,9093],{"class":3273},[1115,9444,9096],{"class":3280},[3261,9446,9449],{"className":9447,"code":9448,"language":4279,"meta":3265},[4277],"    Pearson's Chi-squared test\n\ndata:  tab2\nX-squared = 6.8677, df = 2, p-value = 0.03226\n\n          vzdelani\nzverejnuje       SS       VS      ZS\n       ne  18.73303 25.39367 47.8733\n       ano 26.26697 35.60633 67.1267\n",[1434,9450,9448],{"__ignoreMap":3265},[1110,9452,9453,9454,9129,9477,9490,9491,4984,9510,9527,9528,1247],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,9455,9457],{"className":9456},[1136],[1138,9458,9459],{"xmlns":1140},[1142,9460,9461,9474],{},[1145,9462,9463,9469,9471],{},[5465,9464,9465,9467],{},[1156,9466,6817],{},[1919,9468,2302],{},[1148,9470,1914],{},[1919,9472,9473],{},"6,87",[1172,9475,9476],{"encoding":1174},"\\chi^2 = 6{,}87",[1115,9478,9480],{"className":9479},[1136],[1138,9481,9482],{"xmlns":1140},[1142,9483,9484,9488],{},[1145,9485,9486],{},[1919,9487,2302],{},[1172,9489,2302],{"encoding":1174}," stupni volnosti dává\np-hodnotu ",[1115,9492,9494],{"className":9493},[1136],[1138,9495,9496],{"xmlns":1140},[1142,9497,9498,9507],{},[1145,9499,9500,9503,9505],{},[1919,9501,9502],{},"0,032",[1148,9504,5682],{},[1919,9506,9160],{},[1172,9508,9509],{"encoding":1174},"0{,}032 \u003C 0{,}05",[1115,9511,9513],{"className":9512},[1136],[1138,9514,9515],{"xmlns":1140},[1142,9516,9517,9525],{},[1145,9518,9519],{},[1217,9520,9521,9523],{},[1156,9522,6797],{},[1919,9524,2780],{},[1172,9526,6802],{"encoding":1174}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1445,9529,9530],{},"závisí",[1110,9532,9533,9534,9551],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,9535,9537],{"className":9536},[1136],[1138,9538,9539],{"xmlns":1140},[1142,9540,9541,9549],{},[1145,9542,9543],{},[1217,9544,9545,9547],{},[1156,9546,6797],{},[1919,9548,2780],{},[1172,9550,6802],{"encoding":1174}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,9553,9554],{},[1527,9555],{"alt":9556,"className":9557,"src":9558},"mask-kt-observed-expected",[1531,1532],"\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,9560,9561,9562,9579,9580,2529],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,9563,9565],{"className":9564},[1136],[1138,9566,9567],{"xmlns":1140},[1142,9568,9569,9577],{},[1145,9570,9571],{},[5465,9572,9573,9575],{},[1156,9574,6817],{},[1919,9576,2302],{},[1172,9578,6822],{"encoding":1174}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,9581,9583],{"className":9582},[1136],[1138,9584,9585],{"xmlns":1140},[1142,9586,9587,9591],{},[1145,9588,9589],{},[1156,9590,6835],{},[1172,9592,6835],{"encoding":1174},[1110,9594,9595],{},[1527,9596],{"alt":9597,"className":9598,"src":9599},"mask-kt-chi2-kriticky-obor",[1531,1532],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1437,9601,6883],{"id":9602},"cramérův-koeficient-kontingence",[1110,9604,9605,9606,2529],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1445,9607,9608],{},"Cramérův koeficient\nkontingence",[1115,9610,9612],{"className":9611},[1136],[1138,9613,9614],{"xmlns":1140,"display":1897},[1142,9615,9616,9668],{},[1145,9617,9618,9620,9622,9646,9648,9650,9652,9654,9656,9658,9660,9662,9664,9666],{},[1156,9619,6896],{},[1148,9621,1914],{},[5460,9623,9624],{},[1916,9625,9626,9632],{},[5465,9627,9628,9630],{},[1156,9629,6817],{},[1919,9631,2302],{},[1145,9633,9634,9636,9638,9640,9642,9644],{},[1156,9635,1292],{},[1148,9637,1151],{"stretchy":1150},[1156,9639,1379],{},[1148,9641,1990],{},[1919,9643,1921],{},[1148,9645,1170],{"stretchy":1150},[1148,9647,1164],{"separator":1121},[1954,9649],{"width":1956},[1156,9651,1379],{},[1148,9653,1914],{},[1156,9655,1997],{},[1148,9657,1975],{},[1148,9659,1151],{"stretchy":1150},[1156,9661,71],{},[1148,9663,1164],{"separator":1121},[1156,9665,1198],{},[1148,9667,1170],{"stretchy":1150},[1172,9669,9670],{"encoding":1174},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,9672,9673,9674,9691,9692,9710,9711,9729],{},"kde ",[1115,9675,9677],{"className":9676},[1136],[1138,9678,9679],{"xmlns":1140},[1142,9680,9681,9689],{},[1145,9682,9683],{},[5465,9684,9685,9687],{},[1156,9686,6817],{},[1919,9688,2302],{},[1172,9690,6822],{"encoding":1174}," je hodnota testového kritéria z testu nezávislosti. ",[1115,9693,9695],{"className":9694},[1136],[1138,9696,9697],{"xmlns":1140},[1142,9698,9699,9707],{},[1145,9700,9701,9703,9705],{},[1156,9702,6896],{},[1148,9704,1914],{},[1919,9706,2780],{},[1172,9708,9709],{"encoding":1174},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,9712,9714],{"className":9713},[1136],[1138,9715,9716],{"xmlns":1140},[1142,9717,9718,9726],{},[1145,9719,9720,9722,9724],{},[1156,9721,6896],{},[1148,9723,1914],{},[1919,9725,1921],{},[1172,9727,9728],{"encoding":1174},"V = 1"," jejich úplné závislosti.",[3261,9731,9733],{"className":3263,"code":9732,"language":71,"meta":3265,"style":3265},"V1 \u003C- sqrt(as.numeric(chisq.test(tab1)$statistic) \u002F (sum(tab1) * (min(dim(tab1)) - 1)))\nV2 \u003C- sqrt(as.numeric(chisq.test(tab2)$statistic) \u002F (sum(tab2) * (min(dim(tab2)) - 1)))\nV1\nV2\n",[1434,9734,9735,9804,9867,9872],{"__ignoreMap":3265},[1115,9736,9737,9740,9742,9744,9746,9749,9751,9753,9755,9757,9759,9761,9764,9766,9768,9770,9773,9775,9777,9779,9782,9784,9786,9788,9791,9793,9795,9798,9800,9802],{"class":3270,"line":10},[1115,9738,9739],{"class":3280},"V1",[1115,9741,3291],{"class":3273},[1115,9743,6158],{"class":3294},[1115,9745,1151],{"class":3277},[1115,9747,9748],{"class":3294},"as.numeric",[1115,9750,1151],{"class":3277},[1115,9752,9074],{"class":3294},[1115,9754,1151],{"class":3277},[1115,9756,8896],{"class":3280},[1115,9758,1170],{"class":3277},[1115,9760,9093],{"class":3273},[1115,9762,9763],{"class":3280},"statistic",[1115,9765,6207],{"class":3277},[1115,9767,4412],{"class":3273},[1115,9769,6173],{"class":3277},[1115,9771,9772],{"class":3294},"sum",[1115,9774,1151],{"class":3277},[1115,9776,8896],{"class":3280},[1115,9778,6207],{"class":3277},[1115,9780,9781],{"class":3273},"*",[1115,9783,6173],{"class":3277},[1115,9785,1997],{"class":3294},[1115,9787,1151],{"class":3277},[1115,9789,9790],{"class":3294},"dim",[1115,9792,1151],{"class":3277},[1115,9794,8896],{"class":3280},[1115,9796,9797],{"class":3277},")) ",[1115,9799,6343],{"class":3273},[1115,9801,3882],{"class":3312},[1115,9803,9068],{"class":3277},[1115,9805,9806,9809,9811,9813,9815,9817,9819,9821,9823,9825,9827,9829,9831,9833,9835,9837,9839,9841,9843,9845,9847,9849,9851,9853,9855,9857,9859,9861,9863,9865],{"class":3270,"line":27},[1115,9807,9808],{"class":3280},"V2",[1115,9810,3291],{"class":3273},[1115,9812,6158],{"class":3294},[1115,9814,1151],{"class":3277},[1115,9816,9748],{"class":3294},[1115,9818,1151],{"class":3277},[1115,9820,9074],{"class":3294},[1115,9822,1151],{"class":3277},[1115,9824,9302],{"class":3280},[1115,9826,1170],{"class":3277},[1115,9828,9093],{"class":3273},[1115,9830,9763],{"class":3280},[1115,9832,6207],{"class":3277},[1115,9834,4412],{"class":3273},[1115,9836,6173],{"class":3277},[1115,9838,9772],{"class":3294},[1115,9840,1151],{"class":3277},[1115,9842,9302],{"class":3280},[1115,9844,6207],{"class":3277},[1115,9846,9781],{"class":3273},[1115,9848,6173],{"class":3277},[1115,9850,1997],{"class":3294},[1115,9852,1151],{"class":3277},[1115,9854,9790],{"class":3294},[1115,9856,1151],{"class":3277},[1115,9858,9302],{"class":3280},[1115,9860,9797],{"class":3277},[1115,9862,6343],{"class":3273},[1115,9864,3882],{"class":3312},[1115,9866,9068],{"class":3277},[1115,9868,9869],{"class":3270,"line":148},[1115,9870,9871],{"class":3280},"V1\n",[1115,9873,9874],{"class":3270,"line":111},[1115,9875,9876],{"class":3280},"V2\n",[3261,9878,9881],{"className":9879,"code":9880,"language":4279,"meta":3265},[4277],"[1] 0.08441958\n[1] 0.1762822\n",[1434,9882,9880],{"__ignoreMap":3265},[1110,9884,9885],{},[1527,9886],{"alt":9887,"className":9888,"src":9889},"mask-kt-cramerovo-v",[1531,1532],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,9891,9892,9893,9912,9913,9930,9931,4984,9950,9967],{},"U nákupu potravin je ",[1115,9894,9896],{"className":9895},[1136],[1138,9897,9898],{"xmlns":1140},[1142,9899,9900,9909],{},[1145,9901,9902,9904,9906],{},[1156,9903,6896],{},[1148,9905,1914],{},[1919,9907,9908],{},"0,084",[1172,9910,9911],{"encoding":1174},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,9914,9916],{"className":9915},[1136],[1138,9917,9918],{"xmlns":1140},[1142,9919,9920,9928],{},[1145,9921,9922],{},[1217,9923,9924,9926],{},[1156,9925,6797],{},[1919,9927,2780],{},[1172,9929,6802],{"encoding":1174}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,9932,9934],{"className":9933},[1136],[1138,9935,9936],{"xmlns":1140},[1142,9937,9938,9947],{},[1145,9939,9940,9942,9944],{},[1156,9941,6896],{},[1148,9943,1914],{},[1919,9945,9946],{},"0,176",[1172,9948,9949],{"encoding":1174},"V = 0{,}176",[1115,9951,9953],{"className":9952},[1136],[1138,9954,9955],{"xmlns":1140},[1142,9956,9957,9965],{},[1145,9958,9959],{},[1217,9960,9961,9963],{},[1156,9962,6797],{},[1919,9964,2780],{},[1172,9966,6802],{"encoding":1174},"\njsme zamítli, ale samotná závislost je stále slabá.",[1437,9969,6903],{"id":9970},"čtyřpolní-tabulka",[1110,9972,9973,9975,9976,9989,9990,10003,10004,10026],{},[1445,9974,6903],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,9977,9979],{"className":9978},[1136],[1138,9980,9981],{"xmlns":1140},[1142,9982,9983,9987],{},[1145,9984,9985],{},[1156,9986,7001],{},[1172,9988,7001],{"encoding":1174}," i ",[1115,9991,9993],{"className":9992},[1136],[1138,9994,9995],{"xmlns":1140},[1142,9996,9997,10001],{},[1145,9998,9999],{},[1156,10000,7047],{},[1172,10002,7047],{"encoding":1174}," mají jen dvě varianty\n(",[1115,10005,10007],{"className":10006},[1136],[1138,10008,10009],{"xmlns":1140},[1142,10010,10011,10023],{},[1145,10012,10013,10015,10017,10019,10021],{},[1156,10014,71],{},[1148,10016,1914],{},[1156,10018,1198],{},[1148,10020,1914],{},[1919,10022,2302],{},[1172,10024,10025],{"encoding":1174},"r = s = 2","):",[1459,10028,10029,10113],{},[1462,10030,10031],{},[1465,10032,10033,10052,10071,10090],{},[1468,10034,10035],{},[1115,10036,10038],{"className":10037},[1136],[1138,10039,10040],{"xmlns":1140},[1142,10041,10042,10050],{},[1145,10043,10044,10046,10048],{},[1156,10045,7001],{},[1156,10047,7332],{"mathvariant":2014},[1156,10049,7047],{},[1172,10051,7337],{"encoding":1174},[1468,10053,10054],{},[1115,10055,10057],{"className":10056},[1136],[1138,10058,10059],{"xmlns":1140},[1142,10060,10061,10069],{},[1145,10062,10063],{},[1217,10064,10065,10067],{},[1156,10066,7047],{},[1919,10068,1921],{},[1172,10070,7357],{"encoding":1174},[1468,10072,10073],{},[1115,10074,10076],{"className":10075},[1136],[1138,10077,10078],{"xmlns":1140},[1142,10079,10080,10088],{},[1145,10081,10082],{},[1217,10083,10084,10086],{},[1156,10085,7047],{},[1919,10087,2302],{},[1172,10089,7377],{"encoding":1174},[1468,10091,10092],{},[1115,10093,10095],{"className":10094},[1136],[1138,10096,10097],{"xmlns":1140},[1142,10098,10099,10111],{},[1145,10100,10101],{},[1217,10102,10103,10105],{},[1156,10104,1292],{},[1145,10106,10107,10109],{},[1156,10108,1223],{},[1148,10110,7195],{},[1172,10112,7423],{"encoding":1174},[1477,10114,10115,10197,10279],{},[1465,10116,10117,10136,10155,10174],{},[1482,10118,10119],{},[1115,10120,10122],{"className":10121},[1136],[1138,10123,10124],{"xmlns":1140},[1142,10125,10126,10134],{},[1145,10127,10128],{},[1217,10129,10130,10132],{},[1156,10131,7001],{},[1919,10133,1921],{},[1172,10135,7447],{"encoding":1174},[1482,10137,10138],{},[1115,10139,10141],{"className":10140},[1136],[1138,10142,10143],{"xmlns":1140},[1142,10144,10145,10153],{},[1145,10146,10147],{},[1217,10148,10149,10151],{},[1156,10150,1292],{},[1919,10152,2644],{},[1172,10154,7467],{"encoding":1174},[1482,10156,10157],{},[1115,10158,10160],{"className":10159},[1136],[1138,10161,10162],{"xmlns":1140},[1142,10163,10164,10172],{},[1145,10165,10166],{},[1217,10167,10168,10170],{},[1156,10169,1292],{},[1919,10171,7485],{},[1172,10173,7488],{"encoding":1174},[1482,10175,10176],{},[1115,10177,10179],{"className":10178},[1136],[1138,10180,10181],{"xmlns":1140},[1142,10182,10183,10195],{},[1145,10184,10185],{},[1217,10186,10187,10189],{},[1156,10188,1292],{},[1145,10190,10191,10193],{},[1919,10192,1921],{},[1148,10194,7195],{},[1172,10196,7538],{"encoding":1174},[1465,10198,10199,10218,10237,10256],{},[1482,10200,10201],{},[1115,10202,10204],{"className":10203},[1136],[1138,10205,10206],{"xmlns":1140},[1142,10207,10208,10216],{},[1145,10209,10210],{},[1217,10211,10212,10214],{},[1156,10213,7001],{},[1919,10215,2302],{},[1172,10217,7560],{"encoding":1174},[1482,10219,10220],{},[1115,10221,10223],{"className":10222},[1136],[1138,10224,10225],{"xmlns":1140},[1142,10226,10227,10235],{},[1145,10228,10229],{},[1217,10230,10231,10233],{},[1156,10232,1292],{},[1919,10234,7578],{},[1172,10236,7581],{"encoding":1174},[1482,10238,10239],{},[1115,10240,10242],{"className":10241},[1136],[1138,10243,10244],{"xmlns":1140},[1142,10245,10246,10254],{},[1145,10247,10248],{},[1217,10249,10250,10252],{},[1156,10251,1292],{},[1919,10253,7599],{},[1172,10255,7602],{"encoding":1174},[1482,10257,10258],{},[1115,10259,10261],{"className":10260},[1136],[1138,10262,10263],{"xmlns":1140},[1142,10264,10265,10277],{},[1145,10266,10267],{},[1217,10268,10269,10271],{},[1156,10270,1292],{},[1145,10272,10273,10275],{},[1919,10274,2302],{},[1148,10276,7195],{},[1172,10278,7652],{"encoding":1174},[1465,10280,10281,10304,10327,10350],{},[1482,10282,10283],{},[1115,10284,10286],{"className":10285},[1136],[1138,10287,10288],{"xmlns":1140},[1142,10289,10290,10302],{},[1145,10291,10292],{},[1217,10293,10294,10296],{},[1156,10295,1292],{},[1145,10297,10298,10300],{},[1148,10299,7195],{},[1156,10301,1934],{},[1172,10303,7814],{"encoding":1174},[1482,10305,10306],{},[1115,10307,10309],{"className":10308},[1136],[1138,10310,10311],{"xmlns":1140},[1142,10312,10313,10325],{},[1145,10314,10315],{},[1217,10316,10317,10319],{},[1156,10318,1292],{},[1145,10320,10321,10323],{},[1148,10322,7195],{},[1919,10324,1921],{},[1172,10326,7838],{"encoding":1174},[1482,10328,10329],{},[1115,10330,10332],{"className":10331},[1136],[1138,10333,10334],{"xmlns":1140},[1142,10335,10336,10348],{},[1145,10337,10338],{},[1217,10339,10340,10342],{},[1156,10341,1292],{},[1145,10343,10344,10346],{},[1148,10345,7195],{},[1919,10347,2302],{},[1172,10349,7862],{"encoding":1174},[1482,10351,10352],{},[1115,10353,10355],{"className":10354},[1136],[1138,10356,10357],{"xmlns":1140},[1142,10358,10359,10363],{},[1145,10360,10361],{},[1156,10362,1292],{},[1172,10364,1292],{"encoding":1174},[1110,10366,6926,10367,10385],{},[1115,10368,10370],{"className":10369},[1136],[1138,10371,10372],{"xmlns":1140},[1142,10373,10374,10382],{},[1145,10375,10376,10378,10380],{},[1156,10377,1292],{},[1148,10379,5755],{},[1919,10381,6920],{},[1172,10383,10384],{"encoding":1174},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,10387,10389],{"className":10388},[1136],[1138,10390,10391],{"xmlns":1140,"display":1897},[1142,10392,10393,10487],{},[1145,10394,10395,10401,10403,10405,10407],{},[5465,10396,10397,10399],{},[1156,10398,6817],{},[1919,10400,2302],{},[1148,10402,1914],{},[1156,10404,1292],{},[5009,10406,5011],{},[1916,10408,10409,10445],{},[1145,10410,10411,10413,10419,10425,10427,10433,10439],{},[1148,10412,1151],{"stretchy":1150},[1217,10414,10415,10417],{},[1156,10416,1292],{},[1919,10418,2644],{},[1217,10420,10421,10423],{},[1156,10422,1292],{},[1919,10424,7599],{},[1148,10426,1990],{},[1217,10428,10429,10431],{},[1156,10430,1292],{},[1919,10432,7485],{},[1217,10434,10435,10437],{},[1156,10436,1292],{},[1919,10438,7578],{},[5465,10440,10441,10443],{},[1148,10442,1170],{"stretchy":1150},[1919,10444,2302],{},[1145,10446,10447,10457,10467,10477],{},[1217,10448,10449,10451],{},[1156,10450,1292],{},[1145,10452,10453,10455],{},[1919,10454,1921],{},[1148,10456,7195],{},[1217,10458,10459,10461],{},[1156,10460,1292],{},[1145,10462,10463,10465],{},[1919,10464,2302],{},[1148,10466,7195],{},[1217,10468,10469,10471],{},[1156,10470,1292],{},[1145,10472,10473,10475],{},[1148,10474,7195],{},[1919,10476,1921],{},[1217,10478,10479,10481],{},[1156,10480,1292],{},[1145,10482,10483,10485],{},[1148,10484,7195],{},[1919,10486,2302],{},[1172,10488,10489],{"encoding":1174},"\\chi^2 = n\\,\\frac{(n_{11}n_{22} - n_{12}n_{21})^2}{n_{1\\bullet}n_{2\\bullet}n_{\\bullet 1}n_{\\bullet 2}}",[1110,10491,10492,10493,10553,10554,10590,10591,10594,10595,10598],{},"s kritickým oborem ",[1115,10494,10496],{"className":10495},[1136],[1138,10497,10498],{"xmlns":1140},[1142,10499,10500,10550],{},[1145,10501,10502,10508,10510,10512,10518,10520,10526,10528,10542,10544,10546,10548],{},[1217,10503,10504,10506],{},[1156,10505,6835],{},[1156,10507,8567],{},[1148,10509,1914],{},[1148,10511,8536],{"stretchy":1150},[5465,10513,10514,10516],{},[1156,10515,6817],{},[1919,10517,2302],{},[1148,10519,2529],{},[5465,10521,10522,10524],{},[1156,10523,6817],{},[1919,10525,2302],{},[1148,10527,8553],{},[8555,10529,10530,10532,10540],{},[1156,10531,6817],{},[1145,10533,10534,10536,10538],{},[1919,10535,1921],{},[1148,10537,1990],{},[1156,10539,8567],{},[1919,10541,2302],{},[1148,10543,1151],{"stretchy":1150},[1919,10545,1921],{},[1148,10547,1170],{"stretchy":1150},[1148,10549,8596],{"stretchy":1150},[1172,10551,10552],{"encoding":1174},"W_\\alpha = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}"," — formálně jde o stejný test\nnezávislosti jako výše, jen dosazený do zjednodušeného tvaru pro ",[1115,10555,10557],{"className":10556},[1136],[1138,10558,10559],{"xmlns":1140},[1142,10560,10561,10587],{},[1145,10562,10563,10565,10567,10569,10571,10573,10575,10577,10579,10581,10583,10585],{},[1148,10564,1151],{"stretchy":1150},[1156,10566,71],{},[1148,10568,1990],{},[1919,10570,1921],{},[1148,10572,1170],{"stretchy":1150},[1148,10574,1151],{"stretchy":1150},[1156,10576,1198],{},[1148,10578,1990],{},[1919,10580,1921],{},[1148,10582,1170],{"stretchy":1150},[1148,10584,1914],{},[1919,10586,1921],{},[1172,10588,10589],{"encoding":1174},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[1434,10592,10593],{},"chisq.test(tab, correct = FALSE)",". Bez ",[1434,10596,10597],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1437,10600,6933],{"id":10601},"mcnemarův-test",[1110,10603,10604,10605,10608,10609,10611,10612,10615,10616,10619,10620,10622],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1445,10606,10607],{},"různé"," znaky na stejném souboru. ",[1445,10610,6933],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1445,10613,10614],{},"jeden"," alternativní znak, a to ",[1445,10617,10618],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1445,10621,6929],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,10624,10625],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1459,10627,10628,10662],{},[1462,10629,10630],{},[1465,10631,10632,10635,10637,10639],{},[1468,10633,10634],{},"před \\ po",[1468,10636,5066],{},[1468,10638,1990],{},[1468,10640,10641],{},[1115,10642,10644],{"className":10643},[1136],[1138,10645,10646],{"xmlns":1140},[1142,10647,10648,10660],{},[1145,10649,10650],{},[1217,10651,10652,10654],{},[1156,10653,1292],{},[1145,10655,10656,10658],{},[1156,10657,1223],{},[1148,10659,7195],{},[1172,10661,7423],{"encoding":1174},[1477,10663,10664,10729,10794],{},[1465,10665,10666,10668,10687,10706],{},[1482,10667,5066],{},[1482,10669,10670],{},[1115,10671,10673],{"className":10672},[1136],[1138,10674,10675],{"xmlns":1140},[1142,10676,10677,10685],{},[1145,10678,10679],{},[1217,10680,10681,10683],{},[1156,10682,1292],{},[1919,10684,2644],{},[1172,10686,7467],{"encoding":1174},[1482,10688,10689],{},[1115,10690,10692],{"className":10691},[1136],[1138,10693,10694],{"xmlns":1140},[1142,10695,10696,10704],{},[1145,10697,10698],{},[1217,10699,10700,10702],{},[1156,10701,1292],{},[1919,10703,7485],{},[1172,10705,7488],{"encoding":1174},[1482,10707,10708],{},[1115,10709,10711],{"className":10710},[1136],[1138,10712,10713],{"xmlns":1140},[1142,10714,10715,10727],{},[1145,10716,10717],{},[1217,10718,10719,10721],{},[1156,10720,1292],{},[1145,10722,10723,10725],{},[1919,10724,1921],{},[1148,10726,7195],{},[1172,10728,7538],{"encoding":1174},[1465,10730,10731,10733,10752,10771],{},[1482,10732,1990],{},[1482,10734,10735],{},[1115,10736,10738],{"className":10737},[1136],[1138,10739,10740],{"xmlns":1140},[1142,10741,10742,10750],{},[1145,10743,10744],{},[1217,10745,10746,10748],{},[1156,10747,1292],{},[1919,10749,7578],{},[1172,10751,7581],{"encoding":1174},[1482,10753,10754],{},[1115,10755,10757],{"className":10756},[1136],[1138,10758,10759],{"xmlns":1140},[1142,10760,10761,10769],{},[1145,10762,10763],{},[1217,10764,10765,10767],{},[1156,10766,1292],{},[1919,10768,7599],{},[1172,10770,7602],{"encoding":1174},[1482,10772,10773],{},[1115,10774,10776],{"className":10775},[1136],[1138,10777,10778],{"xmlns":1140},[1142,10779,10780,10792],{},[1145,10781,10782],{},[1217,10783,10784,10786],{},[1156,10785,1292],{},[1145,10787,10788,10790],{},[1919,10789,2302],{},[1148,10791,7195],{},[1172,10793,7652],{"encoding":1174},[1465,10795,10796,10819,10842,10865],{},[1482,10797,10798],{},[1115,10799,10801],{"className":10800},[1136],[1138,10802,10803],{"xmlns":1140},[1142,10804,10805,10817],{},[1145,10806,10807],{},[1217,10808,10809,10811],{},[1156,10810,1292],{},[1145,10812,10813,10815],{},[1148,10814,7195],{},[1156,10816,1934],{},[1172,10818,7814],{"encoding":1174},[1482,10820,10821],{},[1115,10822,10824],{"className":10823},[1136],[1138,10825,10826],{"xmlns":1140},[1142,10827,10828,10840],{},[1145,10829,10830],{},[1217,10831,10832,10834],{},[1156,10833,1292],{},[1145,10835,10836,10838],{},[1148,10837,7195],{},[1919,10839,1921],{},[1172,10841,7838],{"encoding":1174},[1482,10843,10844],{},[1115,10845,10847],{"className":10846},[1136],[1138,10848,10849],{"xmlns":1140},[1142,10850,10851,10863],{},[1145,10852,10853],{},[1217,10854,10855,10857],{},[1156,10856,1292],{},[1145,10858,10859,10861],{},[1148,10860,7195],{},[1919,10862,2302],{},[1172,10864,7862],{"encoding":1174},[1482,10866,10867],{},[1115,10868,10870],{"className":10869},[1136],[1138,10871,10872],{"xmlns":1140},[1142,10873,10874,10878],{},[1145,10875,10876],{},[1156,10877,1292],{},[1172,10879,1292],{"encoding":1174},[1110,10881,10882,10883,1204,10900,10917,10918,10921,10922,1204,10939,10956,10957,10960],{},"Pole ",[1115,10884,10886],{"className":10885},[1136],[1138,10887,10888],{"xmlns":1140},[1142,10889,10890,10898],{},[1145,10891,10892],{},[1217,10893,10894,10896],{},[1156,10895,1292],{},[1919,10897,2644],{},[1172,10899,7467],{"encoding":1174},[1115,10901,10903],{"className":10902},[1136],[1138,10904,10905],{"xmlns":1140},[1142,10906,10907,10915],{},[1145,10908,10909],{},[1217,10910,10911,10913],{},[1156,10912,1292],{},[1919,10914,7599],{},[1172,10916,7602],{"encoding":1174}," jsou ",[1445,10919,10920],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,10923,10925],{"className":10924},[1136],[1138,10926,10927],{"xmlns":1140},[1142,10928,10929,10937],{},[1145,10930,10931],{},[1217,10932,10933,10935],{},[1156,10934,1292],{},[1919,10936,7485],{},[1172,10938,7488],{"encoding":1174},[1115,10940,10942],{"className":10941},[1136],[1138,10943,10944],{"xmlns":1140},[1142,10945,10946,10954],{},[1145,10947,10948],{},[1217,10949,10950,10952],{},[1156,10951,1292],{},[1919,10953,7578],{},[1172,10955,7581],{"encoding":1174}," jsou\n",[1445,10958,10959],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,10962,10963],{},[1527,10964],{"alt":10965,"className":10966,"src":10967},"mask-kt-mcnemar-tabulka",[1531,1532],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,10969,10970],{},[1445,10971,8070],{},[1538,10973,10974,11011,11092,11150],{},[1127,10975,10976,11010],{},[1115,10977,10979],{"className":10978},[1136],[1138,10980,10981],{"xmlns":1140},[1142,10982,10983,11007],{},[1145,10984,10985,10991,10993,10999,11001],{},[1217,10986,10987,10989],{},[1156,10988,6797],{},[1919,10990,2780],{},[1148,10992,2529],{},[1217,10994,10995,10997],{},[1156,10996,1110],{},[1919,10998,7485],{},[1148,11000,1914],{},[1217,11002,11003,11005],{},[1156,11004,1110],{},[1919,11006,7578],{},[1172,11008,11009],{"encoding":1174},"H_0: p_{12} = p_{21}"," — pravděpodobnost přechodu z varianty (+) do (−) je stejná jako pravděpodobnost\npřechodu z (−) do (+); zásah tedy nemá na rozdělení variant žádný vliv.",[1127,11012,8204,11013,11075,11077,11078,11091],{},[1115,11014,11016],{"className":11015},[1136],[1138,11017,11018],{"xmlns":1140,"display":1897},[1142,11019,11020,11072],{},[1145,11021,11022,11028,11030],{},[5465,11023,11024,11026],{},[1156,11025,6817],{},[1919,11027,2302],{},[1148,11029,1914],{},[1916,11031,11032,11056],{},[1145,11033,11034,11036,11042,11044,11050],{},[1148,11035,1151],{"stretchy":1150},[1217,11037,11038,11040],{},[1156,11039,1292],{},[1919,11041,7485],{},[1148,11043,1990],{},[1217,11045,11046,11048],{},[1156,11047,1292],{},[1919,11049,7578],{},[5465,11051,11052,11054],{},[1148,11053,1170],{"stretchy":1150},[1919,11055,2302],{},[1145,11057,11058,11064,11066],{},[1217,11059,11060,11062],{},[1156,11061,1292],{},[1919,11063,7485],{},[1148,11065,5066],{},[1217,11067,11068,11070],{},[1156,11069,1292],{},[1919,11071,7578],{},[1172,11073,11074],{"encoding":1174},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[8362,11076],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,11079,11081],{"className":11080},[1136],[1138,11082,11083],{"xmlns":1140},[1142,11084,11085,11089],{},[1145,11086,11087],{},[1919,11088,1921],{},[1172,11090,1921],{"encoding":1174}," stupni volnosti.",[1127,11093,8520,11094,1247],{},[1115,11095,11097],{"className":11096},[1136],[1138,11098,11099],{"xmlns":1140},[1142,11100,11101,11147],{},[1145,11102,11103,11105,11107,11109,11115,11117,11123,11125,11139,11141,11143,11145],{},[1156,11104,6835],{},[1148,11106,1914],{},[1148,11108,8536],{"stretchy":1150},[5465,11110,11111,11113],{},[1156,11112,6817],{},[1919,11114,2302],{},[1148,11116,2529],{},[5465,11118,11119,11121],{},[1156,11120,6817],{},[1919,11122,2302],{},[1148,11124,8553],{},[8555,11126,11127,11129,11137],{},[1156,11128,6817],{},[1145,11130,11131,11133,11135],{},[1919,11132,1921],{},[1148,11134,1990],{},[1156,11136,8567],{},[1919,11138,2302],{},[1148,11140,1151],{"stretchy":1150},[1919,11142,1921],{},[1148,11144,1170],{"stretchy":1150},[1148,11146,8596],{"stretchy":1150},[1172,11148,11149],{"encoding":1174},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1127,11151,8602,11152,11165,11166,11183,11184,11201],{},[1115,11153,11155],{"className":11154},[1136],[1138,11156,11157],{"xmlns":1140},[1142,11158,11159,11163],{},[1145,11160,11161],{},[1156,11162,6835],{},[1172,11164,6835],{"encoding":1174},", zamítáme ",[1115,11167,11169],{"className":11168},[1136],[1138,11170,11171],{"xmlns":1140},[1142,11172,11173,11181],{},[1145,11174,11175],{},[1217,11176,11177,11179],{},[1156,11178,6797],{},[1919,11180,2780],{},[1172,11182,6802],{"encoding":1174}," a přijímáme ",[1115,11185,11187],{"className":11186},[1136],[1138,11188,11189],{"xmlns":1140},[1142,11190,11191,11199],{},[1145,11192,11193],{},[1217,11194,11195,11197],{},[1156,11196,6797],{},[1919,11198,1921],{},[1172,11200,8200],{"encoding":1174},": zásah rozdělení variant změnil.",[1110,11203,11204,11205,11208,11209,11212,11213,11215],{},"V R počítá tento test funkce ",[1434,11206,11207],{},"mcnemar.test()",". Vzorec výše ",[1445,11210,11211],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[1434,11214,10597],{}," (viz Časté chyby níže).",[1103,11217,11219,11226,11229,11232,11328],{"className":11218,"dataCallout":2145},[1106,2144],[1110,11220,11222,11225],{"className":11221},[1113],[1115,11223],{"className":11224,"ariaHidden":1121},[1118,2152,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,11227,11228],{},"U 170 studentů bylo zjišťováno, zda zveřejňují své údaje na Facebooku. Poté proběhla informační kampaň o\nrizicích zveřejňování a zjišťování se opakovalo. Posuďte, zda měla kampaň vliv na změnu chování studentů.",[1110,11230,11231],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1459,11233,11234,11269],{},[1462,11235,11236],{},[1465,11237,11238,11240,11243,11246],{},[1468,11239,10634],{},[1468,11241,11242],{},"nezveřejňuje",[1468,11244,11245],{},"zveřejňuje",[1468,11247,11248],{},[1115,11249,11251],{"className":11250},[1136],[1138,11252,11253],{"xmlns":1140},[1142,11254,11255,11267],{},[1145,11256,11257],{},[1217,11258,11259,11261],{},[1156,11260,1292],{},[1145,11262,11263,11265],{},[1156,11264,1223],{},[1148,11266,7195],{},[1172,11268,7423],{"encoding":1174},[1477,11270,11271,11282,11294],{},[1465,11272,11273,11275,11277,11280],{},[1482,11274,11242],{},[1482,11276,8794],{},[1482,11278,11279],{},"68",[1482,11281,2387],{},[1465,11283,11284,11286,11288,11291],{},[1482,11285,11245],{},[1482,11287,9235],{},[1482,11289,11290],{},"50",[1482,11292,11293],{},"78",[1465,11295,11296,11319,11322,11325],{},[1482,11297,11298],{},[1115,11299,11301],{"className":11300},[1136],[1138,11302,11303],{"xmlns":1140},[1142,11304,11305,11317],{},[1145,11306,11307],{},[1217,11308,11309,11311],{},[1156,11310,1292],{},[1145,11312,11313,11315],{},[1148,11314,7195],{},[1156,11316,1934],{},[1172,11318,7814],{"encoding":1174},[1482,11320,11321],{},"52",[1482,11323,11324],{},"118",[1482,11326,11327],{},"170",[1110,11329,11330,11363],{},[1115,11331,11333],{"className":11332},[1136],[1138,11334,11335],{"xmlns":1140},[1142,11336,11337,11361],{},[1145,11338,11339,11345,11347,11353,11355],{},[1217,11340,11341,11343],{},[1156,11342,6797],{},[1919,11344,2780],{},[1148,11346,2529],{},[1217,11348,11349,11351],{},[1156,11350,1110],{},[1919,11352,7485],{},[1148,11354,1914],{},[1217,11356,11357,11359],{},[1156,11358,1110],{},[1919,11360,7578],{},[1172,11362,11009],{"encoding":1174}," — informační kampaň nemá na chování vliv.",[3261,11365,11367],{"className":3263,"code":11366,"language":71,"meta":3265,"style":3265},"tab3 \u003C- matrix(c(24, 68,\n                 28, 50),\n               nrow = 2, byrow = TRUE,\n               dimnames = list(\n                 pred = c(\"nezverejnuje\", \"zverejnuje\"),\n                 po   = c(\"nezverejnuje\", \"zverejnuje\")))\nmcnemar.test(tab3, correct = FALSE)\n",[1434,11368,11369,11393,11407,11425,11435,11458,11477],{"__ignoreMap":3265},[1115,11370,11371,11374,11376,11378,11380,11382,11384,11386,11388,11391],{"class":3270,"line":10},[1115,11372,11373],{"class":3280},"tab3",[1115,11375,3291],{"class":3273},[1115,11377,8901],{"class":3294},[1115,11379,1151],{"class":3277},[1115,11381,1262],{"class":3294},[1115,11383,1151],{"class":3277},[1115,11385,8794],{"class":3312},[1115,11387,1164],{"class":3273},[1115,11389,11390],{"class":3312}," 68",[1115,11392,8922],{"class":3273},[1115,11394,11395,11398,11400,11403,11405],{"class":3270,"line":27},[1115,11396,11397],{"class":3312},"                 28",[1115,11399,1164],{"class":3273},[1115,11401,11402],{"class":3312}," 50",[1115,11404,1170],{"class":3277},[1115,11406,8922],{"class":3273},[1115,11408,11409,11411,11413,11415,11417,11419,11421,11423],{"class":3270,"line":148},[1115,11410,8979],{"class":3280},[1115,11412,3309],{"class":3273},[1115,11414,4156],{"class":3312},[1115,11416,1164],{"class":3273},[1115,11418,8988],{"class":3280},[1115,11420,3309],{"class":3273},[1115,11422,3313],{"class":3312},[1115,11424,8922],{"class":3273},[1115,11426,11427,11429,11431,11433],{"class":3270,"line":111},[1115,11428,8999],{"class":3280},[1115,11430,3309],{"class":3273},[1115,11432,9004],{"class":3294},[1115,11434,9007],{"class":3277},[1115,11436,11437,11440,11442,11444,11446,11449,11451,11454,11456],{"class":3270,"line":96},[1115,11438,11439],{"class":3280},"                 pred",[1115,11441,3309],{"class":3273},[1115,11443,4142],{"class":3294},[1115,11445,1151],{"class":3277},[1115,11447,11448],{"class":3300},"\"nezverejnuje\"",[1115,11450,1164],{"class":3273},[1115,11452,11453],{"class":3300}," \"zverejnuje\"",[1115,11455,1170],{"class":3277},[1115,11457,8922],{"class":3273},[1115,11459,11460,11463,11465,11467,11469,11471,11473,11475],{"class":3270,"line":89},[1115,11461,11462],{"class":3280},"                 po",[1115,11464,9403],{"class":3273},[1115,11466,4142],{"class":3294},[1115,11468,1151],{"class":3277},[1115,11470,11448],{"class":3300},[1115,11472,1164],{"class":3273},[1115,11474,11453],{"class":3300},[1115,11476,9068],{"class":3277},[1115,11478,11479,11482,11484,11486,11488,11491,11493,11496],{"class":3270,"line":82},[1115,11480,11481],{"class":3294},"mcnemar.test",[1115,11483,1151],{"class":3277},[1115,11485,11373],{"class":3280},[1115,11487,1164],{"class":3273},[1115,11489,11490],{"class":3280}," correct",[1115,11492,3309],{"class":3273},[1115,11494,11495],{"class":3312}," FALSE",[1115,11497,3283],{"class":3277},[3261,11499,11502],{"className":11500,"code":11501,"language":4279,"meta":3265},[4277],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[1434,11503,11501],{"__ignoreMap":3265},[1110,11505,11506,11507,4984,11526,11543,11544,11561],{},"P-hodnota ",[1115,11508,11510],{"className":11509},[1136],[1138,11511,11512],{"xmlns":1140},[1142,11513,11514,11523],{},[1145,11515,11516,11519,11521],{},[1919,11517,11518],{},"0,00004456",[1148,11520,5682],{},[1919,11522,9160],{},[1172,11524,11525],{"encoding":1174},"0{,}00004456 \u003C 0{,}05",[1115,11527,11529],{"className":11528},[1136],[1138,11530,11531],{"xmlns":1140},[1142,11532,11533,11541],{},[1145,11534,11535],{},[1217,11536,11537,11539],{},[1156,11538,6797],{},[1919,11540,2780],{},[1172,11542,6802],{"encoding":1174}," zamítáme, přijímáme ",[1115,11545,11547],{"className":11546},[1136],[1138,11548,11549],{"xmlns":1140},[1142,11550,11551,11559],{},[1145,11552,11553],{},[1217,11554,11555,11557],{},[1156,11556,6797],{},[1919,11558,1921],{},[1172,11560,8200],{"encoding":1174}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1437,11563,6378],{"id":6377},[1103,11565,11569,11577],{"className":11566,"dataCallout":11568},[1106,11567],"callout-warning","warning",[1110,11570,11572,11576],{"className":11571},[1113],[1115,11573],{"className":11574,"ariaHidden":1121},[1118,11575,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,11578,11579,11580,11582],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[1434,11581,8673],{}," na ní předpokládá dva nezávislé\nvýběry a ignoruje, že jde o tytéž studenty měřené dvakrát. Na datech z předchozího příkladu to vede k úplně\njinému (a chybnému) závěru.",[3261,11584,11586],{"className":3263,"code":11585,"language":71,"meta":3265,"style":3265},"chisq.test(tab3)\n",[1434,11587,11588],{"__ignoreMap":3265},[1115,11589,11590,11592,11594,11596],{"class":3270,"line":10},[1115,11591,9074],{"class":3294},[1115,11593,1151],{"class":3277},[1115,11595,11373],{"class":3280},[1115,11597,3283],{"class":3277},[3261,11599,11602],{"className":11600,"code":11601,"language":4279,"meta":3265},[4277],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[1434,11603,11601],{"__ignoreMap":3265},[1110,11605,11506,11606,11625,11626,11643,11644,11646,11647,1247],{},[1115,11607,11609],{"className":11608},[1136],[1138,11610,11611],{"xmlns":1140},[1142,11612,11613,11622],{},[1145,11614,11615,11618,11620],{},[1919,11616,11617],{},"0,224",[1148,11619,5755],{},[1919,11621,9160],{},[1172,11623,11624],{"encoding":1174},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,11627,11629],{"className":11628},[1136],[1138,11630,11631],{"xmlns":1140},[1142,11632,11633,11641],{},[1145,11634,11635],{},[1217,11636,11637,11639],{},[1156,11638,6797],{},[1919,11640,2780],{},[1172,11642,6802],{"encoding":1174}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[1434,11645,11207],{},", nikdy ",[1434,11648,8673],{},[1103,11650,11652,11661],{"className":11651,"dataCallout":11568},[1106,11567],[1110,11653,11655,11658,11659],{"className":11654},[1113],[1115,11656],{"className":11657,"ariaHidden":1121},[1118,11575,1120],"Výchozí korekce na kontinuitu v ",[1434,11660,11207],{},[1110,11662,11663,11664,11667],{},"Bez argumentu ",[1434,11665,11666],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3261,11669,11671],{"className":3263,"code":11670,"language":71,"meta":3265,"style":3265},"mcnemar.test(tab3)\n",[1434,11672,11673],{"__ignoreMap":3265},[1115,11674,11675,11677,11679,11681],{"class":3270,"line":10},[1115,11676,11481],{"class":3294},[1115,11678,1151],{"class":3277},[1115,11680,11373],{"class":3280},[1115,11682,3283],{"class":3277},[3261,11684,11687],{"className":11685,"code":11686,"language":4279,"meta":3265},[4277],"    McNemar's Chi-squared test with continuity correction\n\ndata:  tab3\nMcNemar's chi-squared = 15.844, df = 1, p-value = 6.879e-05\n",[1434,11688,11686],{"__ignoreMap":3265},[1110,11690,11691,11692,11710,11711,11730,11731,11744,11745,1247],{},"Oproti nekorigované hodnotě ",[1115,11693,11695],{"className":11694},[1136],[1138,11696,11697],{"xmlns":1140},[1142,11698,11699,11707],{},[1145,11700,11701,11703,11705],{},[1156,11702,1110],{},[1148,11704,1914],{},[1919,11706,11518],{},[1172,11708,11709],{"encoding":1174},"p = 0{,}00004456"," vyjde ",[1115,11712,11714],{"className":11713},[1136],[1138,11715,11716],{"xmlns":1140},[1142,11717,11718,11727],{},[1145,11719,11720,11722,11724],{},[1156,11721,1110],{},[1148,11723,1914],{},[1919,11725,11726],{},"0,00006879",[1172,11728,11729],{"encoding":1174},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,11732,11734],{"className":11733},[1136],[1138,11735,11736],{"xmlns":1140},[1142,11737,11738,11742],{},[1145,11739,11740],{},[1156,11741,8567],{},[1172,11743,8630],{"encoding":1174}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[1434,11746,11747],{},"mcnemar.test(x, correct = FALSE)",[1437,11749,6607],{"id":6606},[1124,11751,11752,11757,11763,11769,11775,11781,11788],{},[1127,11753,11754],{},[6613,11755,6618],{"className":11756,"dataFsResolvedFilePath":6616,"href":6617},[1531],[1127,11758,11759],{},[6613,11760,11762],{"className":11761,"dataFsResolvedFilePath":6639,"href":6640},[1531],"Testování statistických hypotéz",[1127,11764,11765],{},[6613,11766,11768],{"className":11767,"dataFsResolvedFilePath":6624,"href":6625},[1531],"Popisná statistika a datové soubory",[1127,11770,11771],{},[6613,11772,11774],{"className":11773,"dataFsResolvedFilePath":6631,"href":6632},[1531],"Náhodné veličiny a rozdělení pravděpodobnosti",[1127,11776,11777],{},[6613,11778,11780],{"className":11779,"dataFsResolvedFilePath":6646,"href":6647},[1531],"Regresní a korelační analýza",[1127,11782,11783],{},[6613,11784,1094],{"className":11785,"dataFsResolvedFilePath":11786,"href":11787},[1531],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti",[1127,11789,11790],{},[6613,11791,6663],{"className":11792,"dataFsResolvedFilePath":6661,"href":6662},[1531],[1437,11794,6666],{"id":934},[1110,11796,6669,11797,6674],{},[6671,11798,6673],{},[6697,11800,11801],{},"html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: 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05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":11822,"title":11774,"body":11823,"course":23,"courses":6735,"created":6736,"description":3265,"extension":6737,"meta":16253,"navigation":4236,"path":16254,"seo":16255,"sources":16256,"stem":16260,"tags":16261,"type":6748,"updated":6736,"__hash__":16262},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":11824,"toc":16241},[11825,11828,12108,12112,12344,12347,12414,12418,12425,12432,12591,12630,12633,12867,12870,12948,13002,13100,13104,13206,13209,13213,13219,13275,13278,13286,13435,13442,13495,13525,13644,13647,13695,13857,13912,13919,14025,14087,14091,14194,14197,14234,14240,14299,14348,14355,14389,14395,14398,14446,14453,14514,14520,14523,14587,14594,14632,14638,14641,14645,14671,15002,15040,15094,15220,15226,15230,15237,15256,15361,15405,15424,15519,15536,15578,15753,15760,15763,15766,15920,15923,15998,16004,16006,16192,16194,16232,16234,16238],[1099,11826,11774],{"id":11827},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,11829,11831,11837],{"className":11830,"dataCallout":1108},[1106,1107],[1110,11832,11834,1122],{"className":11833},[1113],[1115,11835],{"className":11836,"ariaHidden":1121},[1118,1119,1120],[1124,11838,11839,11850,11951,12018,12096],{},[1127,11840,11841,11842,11845,11846,11849],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1445,11843,11844],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1445,11847,11848],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1127,11851,11852,11853,6884,11856,11892,11893,4560,11930,11950],{},"Každou náhodnou veličinu popisuje ",[1445,11854,11855],{},"distribuční funkce",[1115,11857,11859],{"className":11858},[1136],[1138,11860,11861],{"xmlns":1140},[1142,11862,11863,11889],{},[1145,11864,11865,11868,11870,11872,11874,11876,11878,11880,11882,11885,11887],{},[1156,11866,11867],{},"F",[1148,11869,1151],{"stretchy":1150},[1156,11871,1158],{},[1148,11873,1170],{"stretchy":1150},[1148,11875,1914],{},[1156,11877,5126],{},[1148,11879,1151],{"stretchy":1150},[1156,11881,2168],{},[1148,11883,11884],{},"≤",[1156,11886,1158],{},[1148,11888,1170],{"stretchy":1150},[1172,11890,11891],{"encoding":1174},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,11894,11896],{"className":11895},[1136],[1138,11897,11898],{"xmlns":1140},[1142,11899,11900,11927],{},[1145,11901,11902,11910,11912,11914,11916,11918,11921,11923,11925],{},[5465,11903,11904,11906],{},[1156,11905,11867],{},[1148,11907,11909],{"mathvariant":2014,"lspace":11908,"rspace":11908},"0em","′",[1148,11911,1151],{"stretchy":1150},[1156,11913,1158],{},[1148,11915,1170],{"stretchy":1150},[1148,11917,1914],{},[1156,11919,11920],{},"f",[1148,11922,1151],{"stretchy":1150},[1156,11924,1158],{},[1148,11926,1170],{"stretchy":1150},[1172,11928,11929],{"encoding":1174},"F'(x) = f(x)",[1115,11931,11933],{"className":11932},[1136],[1138,11934,11935],{"xmlns":1140},[1142,11936,11937,11947],{},[1145,11938,11939,11941,11943,11945],{},[1156,11940,11920],{},[1148,11942,1151],{"stretchy":1150},[1156,11944,1158],{},[1148,11946,1170],{"stretchy":1150},[1172,11948,11949],{"encoding":1174},"f(x)"," je hustota pravděpodobnosti.",[1127,11952,11953,11954,1247],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,11955,11957],{"className":11956},[1136],[1138,11958,11959],{"xmlns":1140},[1142,11960,11961,12015],{},[1145,11962,11963,11965,11967,11973,11975,11977,11979,11985,11987,11989,11991,11993,11999,12001,12003,12005,12007,12013],{},[1156,11964,5126],{},[1148,11966,1151],{"stretchy":1150},[1217,11968,11969,11971],{},[1156,11970,1158],{},[1919,11972,1921],{},[1148,11974,5682],{},[1156,11976,2168],{},[1148,11978,5682],{},[1217,11980,11981,11983],{},[1156,11982,1158],{},[1919,11984,2302],{},[1148,11986,1170],{"stretchy":1150},[1148,11988,1914],{},[1156,11990,11867],{},[1148,11992,1151],{"stretchy":1150},[1217,11994,11995,11997],{},[1156,11996,1158],{},[1919,11998,2302],{},[1148,12000,1170],{"stretchy":1150},[1148,12002,1990],{},[1156,12004,11867],{},[1148,12006,1151],{"stretchy":1150},[1217,12008,12009,12011],{},[1156,12010,1158],{},[1919,12012,1921],{},[1148,12014,1170],{"stretchy":1150},[1172,12016,12017],{"encoding":1174},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1127,12019,12020,6884,12023,12053,12054,1176,12057,1176,12060,12063,12064,12077,12078,1247],{},[1445,12021,12022],{},"Normální rozdělení",[1115,12024,12026],{"className":12025},[1136],[1138,12027,12028],{"xmlns":1140},[1142,12029,12030,12050],{},[1145,12031,12032,12035,12037,12039,12042,12048],{},[1156,12033,12034],{},"N",[1148,12036,1151],{"stretchy":1150},[1156,12038,1677],{},[1148,12040,12041],{"separator":1121},";",[5465,12043,12044,12046],{},[1156,12045,1693],{},[1919,12047,2302],{},[1148,12049,1170],{"stretchy":1150},[1172,12051,12052],{"encoding":1174},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[1434,12055,12056],{},"dnorm",[1434,12058,12059],{},"pnorm",[1434,12061,12062],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,12065,12067],{"className":12066},[1136],[1138,12068,12069],{"xmlns":1140},[1142,12070,12071,12075],{},[1145,12072,12073],{},[1156,12074,1693],{},[1172,12076,1696],{"encoding":1174},", ne rozptyl ",[1115,12079,12081],{"className":12080},[1136],[1138,12082,12083],{"xmlns":1140},[1142,12084,12085,12093],{},[1145,12086,12087],{},[5465,12088,12089,12091],{},[1156,12090,1693],{},[1919,12092,2302],{},[1172,12094,12095],{"encoding":1174},"\\sigma^2",[1127,12097,12098,1176,12101,1204,12104,12107],{},[1445,12099,12100],{},"Studentovo",[1445,12102,12103],{},"Pearsonovo (χ²)",[1445,12105,12106],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1437,12109,12111],{"id":12110},"náhodná-veličina","Náhodná veličina",[1110,12113,12114,12117,12118,12133,12134,6884,12136,12149,12150,12170,12171,4560,12184,12208,12209,1176,12222,1176,12236,12249,12250,1176,12263,1176,12277,12291,12292,12305,12306,12319,12320,1247],{},[6613,12115,6618],{"className":12116,"dataFsResolvedFilePath":6616,"href":6617},[1531]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,12119,12121],{"className":12120},[1136],[1138,12122,12123],{"xmlns":1140},[1142,12124,12125,12130],{},[1145,12126,12127],{},[1156,12128,12129],{"mathvariant":2014},"Ω",[1172,12131,12132],{"encoding":1174},"\\Omega"," přiřazený výsledkům pokusu. ",[1445,12135,12111],{},[1115,12137,12139],{"className":12138},[1136],[1138,12140,12141],{"xmlns":1140},[1142,12142,12143,12147],{},[1145,12144,12145],{},[1156,12146,2168],{},[1172,12148,2168],{"encoding":1174}," je funkce, která prvkům ",[1115,12151,12153],{"className":12152},[1136],[1138,12154,12155],{"xmlns":1140},[1142,12156,12157,12167],{},[1145,12158,12159,12162,12165],{},[1156,12160,12161],{},"ω",[1148,12163,12164],{},"∈",[1156,12166,12129],{"mathvariant":2014},[1172,12168,12169],{"encoding":1174},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,12172,12174],{"className":12173},[1136],[1138,12175,12176],{"xmlns":1140},[1142,12177,12178,12182],{},[1145,12179,12180],{},[1156,12181,1158],{},[1172,12183,1158],{"encoding":1174},[1115,12185,12187],{"className":12186},[1136],[1138,12188,12189],{"xmlns":1140},[1142,12190,12191,12205],{},[1145,12192,12193,12195,12197,12199,12201,12203],{},[1156,12194,1158],{},[1148,12196,1914],{},[1156,12198,2168],{},[1148,12200,1151],{"stretchy":1150},[1156,12202,12161],{},[1148,12204,1170],{"stretchy":1150},[1172,12206,12207],{"encoding":1174},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,12210,12212],{"className":12211},[1136],[1138,12213,12214],{"xmlns":1140},[1142,12215,12216,12220],{},[1145,12217,12218],{},[1156,12219,2168],{},[1172,12221,2168],{"encoding":1174},[1115,12223,12225],{"className":12224},[1136],[1138,12226,12227],{"xmlns":1140},[1142,12228,12229,12234],{},[1145,12230,12231],{},[1156,12232,12233],{},"Y",[1172,12235,12233],{"encoding":1174},[1115,12237,12239],{"className":12238},[1136],[1138,12240,12241],{"xmlns":1140},[1142,12242,12243,12247],{},[1145,12244,12245],{},[1156,12246,5427],{},[1172,12248,5427],{"encoding":1174},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,12251,12253],{"className":12252},[1136],[1138,12254,12255],{"xmlns":1140},[1142,12256,12257,12261],{},[1145,12258,12259],{},[1156,12260,1158],{},[1172,12262,1158],{"encoding":1174},[1115,12264,12266],{"className":12265},[1136],[1138,12267,12268],{"xmlns":1140},[1142,12269,12270,12275],{},[1145,12271,12272],{},[1156,12273,12274],{},"y",[1172,12276,12274],{"encoding":1174},[1115,12278,12280],{"className":12279},[1136],[1138,12281,12282],{"xmlns":1140},[1142,12283,12284,12289],{},[1145,12285,12286],{},[1156,12287,12288],{},"t",[1172,12290,12288],{"encoding":1174},"); pravděpodobnost, že ",[1115,12293,12295],{"className":12294},[1136],[1138,12296,12297],{"xmlns":1140},[1142,12298,12299,12303],{},[1145,12300,12301],{},[1156,12302,2168],{},[1172,12304,2168],{"encoding":1174}," nabyla hodnoty ",[1115,12307,12309],{"className":12308},[1136],[1138,12310,12311],{"xmlns":1140},[1142,12312,12313,12317],{},[1145,12314,12315],{},[1156,12316,1158],{},[1172,12318,1158],{"encoding":1174},", zapisujeme ",[1115,12321,12323],{"className":12322},[1136],[1138,12324,12325],{"xmlns":1140},[1142,12326,12327,12341],{},[1145,12328,12329,12331,12333,12335,12337,12339],{},[1156,12330,5126],{},[1148,12332,1151],{"stretchy":1150},[1156,12334,2168],{},[1148,12336,1914],{},[1156,12338,1158],{},[1148,12340,1170],{"stretchy":1150},[1172,12342,12343],{"encoding":1174},"P(X = x)",[1110,12345,12346],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1124,12348,12349,12408],{},[1127,12350,12351,12354,12355,12368,12369,12407],{},[1445,12352,12353],{},"Diskrétní náhodná veličina"," — prvky ",[1115,12356,12358],{"className":12357},[1136],[1138,12359,12360],{"xmlns":1140},[1142,12361,12362,12366],{},[1145,12363,12364],{},[1156,12365,12129],{"mathvariant":2014},[1172,12367,12132],{"encoding":1174}," se zobrazí na osu reálných čísel jako izolované body ",[1115,12370,12372],{"className":12371},[1136],[1138,12373,12374],{"xmlns":1140},[1142,12375,12376,12404],{},[1145,12377,12378,12384,12386,12392,12394,12396,12398],{},[1217,12379,12380,12382],{},[1156,12381,1158],{},[1919,12383,1921],{},[1148,12385,1164],{"separator":1121},[1217,12387,12388,12390],{},[1156,12389,1158],{},[1919,12391,2302],{},[1148,12393,1164],{"separator":1121},[1148,12395,2043],{},[1148,12397,1164],{"separator":1121},[1217,12399,12400,12402],{},[1156,12401,1158],{},[1156,12403,1234],{},[1172,12405,12406],{"encoding":1174},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1127,12409,12410,12413],{},[1445,12411,12412],{},"Spojitá náhodná veličina"," — hodnoty tvoří interval na ose reálných čísel, přičemž každý bod intervalu má nulovou pravděpodobnost. Příklad: velikost výrobku, doba psaní testu, výška dětí v populaci.",[1437,12415,12417],{"id":12416},"distribuční-funkce","Distribuční funkce",[1110,12419,12420,12421,12424],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1445,12422,12423],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,12426,12427],{},[1527,12428],{"alt":12429,"className":12430,"src":12431},"mask-nv-distribucni-funkce",[1531,1532],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,12433,12436,12443],{"className":12434,"dataCallout":654},[1106,12435],"callout-info",[1110,12437,12439,12442],{"className":12438},[1113],[1115,12440],{"className":12441,"ariaHidden":1121},[1118,1119,1120],"Definice",[1110,12444,12445,12446,12459,12460,12480,12481,12494,12495,12531,12550,12551,12564,12565,1247],{},"Distribuční funkcí náhodné veličiny ",[1115,12447,12449],{"className":12448},[1136],[1138,12450,12451],{"xmlns":1140},[1142,12452,12453,12457],{},[1145,12454,12455],{},[1156,12456,2168],{},[1172,12458,2168],{"encoding":1174}," nazýváme reálnou funkci ",[1115,12461,12463],{"className":12462},[1136],[1138,12464,12465],{"xmlns":1140},[1142,12466,12467,12477],{},[1145,12468,12469,12471,12473,12475],{},[1156,12470,11867],{},[1148,12472,1151],{"stretchy":1150},[1156,12474,1158],{},[1148,12476,1170],{"stretchy":1150},[1172,12478,12479],{"encoding":1174},"F(x)"," definovanou pro každé reálné číslo ",[1115,12482,12484],{"className":12483},[1136],[1138,12485,12486],{"xmlns":1140},[1142,12487,12488,12492],{},[1145,12489,12490],{},[1156,12491,1158],{},[1172,12493,1158],{"encoding":1174}," jako\n",[1115,12496,12498],{"className":12497},[1136],[1138,12499,12500],{"xmlns":1140},[1142,12501,12502,12528],{},[1145,12503,12504,12506,12508,12510,12512,12514,12516,12518,12520,12522,12524,12526],{},[1156,12505,11867],{},[1148,12507,1151],{"stretchy":1150},[1156,12509,1158],{},[1148,12511,1170],{"stretchy":1150},[1148,12513,1914],{},[1156,12515,5126],{},[1148,12517,1151],{"stretchy":1150},[1156,12519,2168],{},[1148,12521,11884],{},[1156,12523,1158],{},[1148,12525,1170],{"stretchy":1150},[1156,12527,1247],{"mathvariant":2014},[1172,12529,12530],{"encoding":1174},"F(x) = P(X \\le x).",[1115,12532,12534],{"className":12533},[1136],[1138,12535,12536],{"xmlns":1140},[1142,12537,12538,12548],{},[1145,12539,12540,12542,12544,12546],{},[1156,12541,11867],{},[1148,12543,1151],{"stretchy":1150},[1156,12545,1158],{},[1148,12547,1170],{"stretchy":1150},[1172,12549,12479],{"encoding":1174}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,12552,12554],{"className":12553},[1136],[1138,12555,12556],{"xmlns":1140},[1142,12557,12558,12562],{},[1145,12559,12560],{},[1156,12561,2168],{},[1172,12563,2168],{"encoding":1174}," nabude hodnoty z intervalu ",[1115,12566,12568],{"className":12567},[1136],[1138,12569,12570],{"xmlns":1140},[1142,12571,12572,12588],{},[1145,12573,12574,12576,12578,12581,12583,12585],{},[1148,12575,1151],{"stretchy":1150},[1148,12577,1990],{},[1156,12579,12580],{"mathvariant":2014},"∞",[1148,12582,1164],{"separator":1121},[1156,12584,1158],{},[1148,12586,12587],{"stretchy":1150},"⟩",[1172,12589,12590],{"encoding":1174},"(-\\infty, x\\rangle",[1110,12592,12593,12594,12607,12608,12629],{},"Značí-li například ",[1115,12595,12597],{"className":12596},[1136],[1138,12598,12599],{"xmlns":1140},[1142,12600,12601,12605],{},[1145,12602,12603],{},[1156,12604,2168],{},[1172,12606,2168],{"encoding":1174}," výšku mužů v populaci, pak ",[1115,12609,12611],{"className":12610},[1136],[1138,12612,12613],{"xmlns":1140},[1142,12614,12615,12626],{},[1145,12616,12617,12619,12621,12624],{},[1156,12618,11867],{},[1148,12620,1151],{"stretchy":1150},[1919,12622,12623],{},"175",[1148,12625,1170],{"stretchy":1150},[1172,12627,12628],{"encoding":1174},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,12631,12632],{},"Pro distribuční funkci vždy platí:",[1124,12634,12635,12665,12723,12783],{},[1127,12636,12637,1164],{},[1115,12638,12640],{"className":12639},[1136],[1138,12641,12642],{"xmlns":1140},[1142,12643,12644,12662],{},[1145,12645,12646,12648,12650,12652,12654,12656,12658,12660],{},[1919,12647,2780],{},[1148,12649,11884],{},[1156,12651,11867],{},[1148,12653,1151],{"stretchy":1150},[1156,12655,1158],{},[1148,12657,1170],{"stretchy":1150},[1148,12659,11884],{},[1919,12661,1921],{},[1172,12663,12664],{"encoding":1174},"0 \\le F(x) \\le 1",[1127,12666,12667,12668,1164],{},"je neklesající: ",[1115,12669,12671],{"className":12670},[1136],[1138,12672,12673],{"xmlns":1140},[1142,12674,12675,12720],{},[1145,12676,12677,12683,12685,12691,12694,12696,12698,12704,12706,12708,12710,12712,12718],{},[1217,12678,12679,12681],{},[1156,12680,1158],{},[1919,12682,1921],{},[1148,12684,11884],{},[1217,12686,12687,12689],{},[1156,12688,1158],{},[1919,12690,2302],{},[1148,12692,12693],{},"⇒",[1156,12695,11867],{},[1148,12697,1151],{"stretchy":1150},[1217,12699,12700,12702],{},[1156,12701,1158],{},[1919,12703,1921],{},[1148,12705,1170],{"stretchy":1150},[1148,12707,11884],{},[1156,12709,11867],{},[1148,12711,1151],{"stretchy":1150},[1217,12713,12714,12716],{},[1156,12715,1158],{},[1919,12717,2302],{},[1148,12719,1170],{"stretchy":1150},[1172,12721,12722],{"encoding":1174},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1127,12724,12725,12726,1164],{},"je spojitá zprava: ",[1115,12727,12729],{"className":12728},[1136],[1138,12730,12731],{"xmlns":1140},[1142,12732,12733,12780],{},[1145,12734,12735,12758,12760,12762,12764,12766,12768,12770,12772,12774,12776,12778],{},[1217,12736,12737,12744],{},[1145,12738,12739,12742],{},[1156,12740,12741],{},"lim",[1148,12743,1975],{},[1145,12745,12746,12749,12752],{},[1156,12747,12748],{},"h",[1148,12750,12751],{},"→",[5465,12753,12754,12756],{},[1919,12755,2780],{},[1148,12757,5066],{},[1156,12759,11867],{},[1148,12761,1151],{"stretchy":1150},[1156,12763,1158],{},[1148,12765,5066],{},[1156,12767,12748],{},[1148,12769,1170],{"stretchy":1150},[1148,12771,1914],{},[1156,12773,11867],{},[1148,12775,1151],{"stretchy":1150},[1156,12777,1158],{},[1148,12779,1170],{"stretchy":1150},[1172,12781,12782],{"encoding":1174},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1127,12784,12785,1176,12827,1247],{},[1115,12786,12788],{"className":12787},[1136],[1138,12789,12790],{"xmlns":1140},[1142,12791,12792,12824],{},[1145,12793,12794,12812,12814,12816,12818,12820,12822],{},[1217,12795,12796,12802],{},[1145,12797,12798,12800],{},[1156,12799,12741],{},[1148,12801,1975],{},[1145,12803,12804,12806,12808,12810],{},[1156,12805,1158],{},[1148,12807,12751],{},[1148,12809,1990],{},[1156,12811,12580],{"mathvariant":2014},[1156,12813,11867],{},[1148,12815,1151],{"stretchy":1150},[1156,12817,1158],{},[1148,12819,1170],{"stretchy":1150},[1148,12821,1914],{},[1919,12823,2780],{},[1172,12825,12826],{"encoding":1174},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,12828,12830],{"className":12829},[1136],[1138,12831,12832],{"xmlns":1140},[1142,12833,12834,12864],{},[1145,12835,12836,12852,12854,12856,12858,12860,12862],{},[1217,12837,12838,12844],{},[1145,12839,12840,12842],{},[1156,12841,12741],{},[1148,12843,1975],{},[1145,12845,12846,12848,12850],{},[1156,12847,1158],{},[1148,12849,12751],{},[1156,12851,12580],{"mathvariant":2014},[1156,12853,11867],{},[1148,12855,1151],{"stretchy":1150},[1156,12857,1158],{},[1148,12859,1170],{"stretchy":1150},[1148,12861,1914],{},[1919,12863,1921],{},[1172,12865,12866],{"encoding":1174},"\\lim_{x \\to \\infty} F(x) = 1",[1110,12868,12869],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,12871,12873],{"className":12872},[1136],[1138,12874,12875],{"xmlns":1140,"display":1897},[1142,12876,12877,12945],{},[1145,12878,12879,12885,12887,12889,12891,12893,12895,12897,12899,12901,12903,12905,12907,12909,12911,12913,12915,12928,12930,12932,12934,12936,12938,12941,12943],{},[5465,12880,12881,12883],{},[1156,12882,11867],{},[1148,12884,11909],{"mathvariant":2014,"lspace":11908,"rspace":11908},[1148,12886,1151],{"stretchy":1150},[1156,12888,1158],{},[1148,12890,1170],{"stretchy":1150},[1148,12892,1914],{},[1156,12894,11920],{},[1148,12896,1151],{"stretchy":1150},[1156,12898,1158],{},[1148,12900,1170],{"stretchy":1150},[1148,12902,1164],{"separator":1121},[1954,12904],{"width":1956},[1156,12906,11867],{},[1148,12908,1151],{"stretchy":1150},[1156,12910,1158],{},[1148,12912,1170],{"stretchy":1150},[1148,12914,1914],{},[8555,12916,12917,12920,12926],{},[1148,12918,12919],{},"∫",[1145,12921,12922,12924],{},[1148,12923,1990],{},[1156,12925,12580],{"mathvariant":2014},[1156,12927,1158],{},[1156,12929,11920],{},[1148,12931,1151],{"stretchy":1150},[1156,12933,12288],{},[1148,12935,1170],{"stretchy":1150},[5009,12937,5011],{},[1156,12939,12940],{},"d",[1156,12942,12288],{},[1156,12944,1247],{"mathvariant":2014},[1172,12946,12947],{"encoding":1174},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,12949,12950,12951,12964,12965,1204,12983,13001],{},"Pravděpodobnost, že ",[1115,12952,12954],{"className":12953},[1136],[1138,12955,12956],{"xmlns":1140},[1142,12957,12958,12962],{},[1145,12959,12960],{},[1156,12961,2168],{},[1172,12963,2168],{"encoding":1174}," padne mezi body ",[1115,12966,12968],{"className":12967},[1136],[1138,12969,12970],{"xmlns":1140},[1142,12971,12972,12980],{},[1145,12973,12974],{},[1217,12975,12976,12978],{},[1156,12977,1158],{},[1919,12979,1921],{},[1172,12981,12982],{"encoding":1174},"x_1",[1115,12984,12986],{"className":12985},[1136],[1138,12987,12988],{"xmlns":1140},[1142,12989,12990,12998],{},[1145,12991,12992],{},[1217,12993,12994,12996],{},[1156,12995,1158],{},[1919,12997,2302],{},[1172,12999,13000],{"encoding":1174},"x_2",", se pak počítá jako",[1115,13003,13005],{"className":13004},[1136],[1138,13006,13007],{"xmlns":1140,"display":1897},[1142,13008,13009,13097],{},[1145,13010,13011,13013,13015,13021,13023,13025,13027,13033,13035,13037,13053,13055,13057,13059,13061,13063,13065,13067,13069,13071,13073,13079,13081,13083,13085,13087,13093,13095],{},[1156,13012,5126],{},[1148,13014,1151],{"stretchy":1150},[1217,13016,13017,13019],{},[1156,13018,1158],{},[1919,13020,1921],{},[1148,13022,5682],{},[1156,13024,2168],{},[1148,13026,5682],{},[1217,13028,13029,13031],{},[1156,13030,1158],{},[1919,13032,2302],{},[1148,13034,1170],{"stretchy":1150},[1148,13036,1914],{},[8555,13038,13039,13041,13047],{},[1148,13040,12919],{},[1217,13042,13043,13045],{},[1156,13044,1158],{},[1919,13046,1921],{},[1217,13048,13049,13051],{},[1156,13050,1158],{},[1919,13052,2302],{},[1156,13054,11920],{},[1148,13056,1151],{"stretchy":1150},[1156,13058,12288],{},[1148,13060,1170],{"stretchy":1150},[5009,13062,5011],{},[1156,13064,12940],{},[1156,13066,12288],{},[1148,13068,1914],{},[1156,13070,11867],{},[1148,13072,1151],{"stretchy":1150},[1217,13074,13075,13077],{},[1156,13076,1158],{},[1919,13078,2302],{},[1148,13080,1170],{"stretchy":1150},[1148,13082,1990],{},[1156,13084,11867],{},[1148,13086,1151],{"stretchy":1150},[1217,13088,13089,13091],{},[1156,13090,1158],{},[1919,13092,1921],{},[1148,13094,1170],{"stretchy":1150},[1156,13096,1247],{"mathvariant":2014},[1172,13098,13099],{"encoding":1174},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1437,13101,13103],{"id":13102},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,13105,13107,13113],{"className":13106,"dataCallout":654},[1106,12435],[1110,13108,13110,12442],{"className":13109},[1113],[1115,13111],{"className":13112,"ariaHidden":1121},[1118,1119,1120],[1110,13114,13115,13116,13135,13136,13149,13150,13163,13164,1247],{},"Hustota pravděpodobnosti ",[1115,13117,13119],{"className":13118},[1136],[1138,13120,13121],{"xmlns":1140},[1142,13122,13123,13133],{},[1145,13124,13125,13127,13129,13131],{},[1156,13126,11920],{},[1148,13128,1151],{"stretchy":1150},[1156,13130,1158],{},[1148,13132,1170],{"stretchy":1150},[1172,13134,11949],{"encoding":1174}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,13137,13139],{"className":13138},[1136],[1138,13140,13141],{"xmlns":1140},[1142,13142,13143,13147],{},[1145,13144,13145],{},[1156,13146,2168],{},[1172,13148,2168],{"encoding":1174}," nahuštěny v okolí bodu ",[1115,13151,13153],{"className":13152},[1136],[1138,13154,13155],{"xmlns":1140},[1142,13156,13157,13161],{},[1145,13158,13159],{},[1156,13160,1158],{},[1172,13162,1158],{"encoding":1174},". Je vždy nezáporná a platí pro ni ",[1115,13165,13167],{"className":13166},[1136],[1138,13168,13169],{"xmlns":1140},[1142,13170,13171,13203],{},[1145,13172,13173,13185,13187,13189,13191,13193,13195,13197,13199,13201],{},[8555,13174,13175,13177,13183],{},[1148,13176,12919],{},[1145,13178,13179,13181],{},[1148,13180,1990],{},[1156,13182,12580],{"mathvariant":2014},[1156,13184,12580],{"mathvariant":2014},[1156,13186,11920],{},[1148,13188,1151],{"stretchy":1150},[1156,13190,1158],{},[1148,13192,1170],{"stretchy":1150},[5009,13194,5011],{},[1156,13196,12940],{},[1156,13198,1158],{},[1148,13200,1914],{},[1919,13202,1921],{},[1172,13204,13205],{"encoding":1174},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,13207,13208],{},"Intuitivně: rozdělíme-li hodnoty náhodné veličiny (např. výšku mužů v populaci) do stejně širokých intervalů, bude v intervalech blízko průměru nahuštěno víc pozorování než v krajních intervalech — hustota tam bude vyšší.",[1437,13210,13212],{"id":13211},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,13214,13215,13218],{},[1445,13216,13217],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,13220,13222],{"className":13221},[1136],[1138,13223,13224],{"xmlns":1140,"display":1897},[1142,13225,13226,13272],{},[1145,13227,13228,13231,13233,13235,13237,13239,13251,13253,13256,13258,13260,13262,13264,13266,13268,13270],{},[1156,13229,13230],{},"E",[1148,13232,1151],{"stretchy":1150},[1156,13234,2168],{},[1148,13236,1170],{"stretchy":1150},[1148,13238,1914],{},[8555,13240,13241,13243,13249],{},[1148,13242,12919],{},[1145,13244,13245,13247],{},[1148,13246,1990],{},[1156,13248,12580],{"mathvariant":2014},[1156,13250,12580],{"mathvariant":2014},[1156,13252,1158],{},[1148,13254,13255],{},"⋅",[1156,13257,11920],{},[1148,13259,1151],{"stretchy":1150},[1156,13261,1158],{},[1148,13263,1170],{"stretchy":1150},[5009,13265,5011],{},[1156,13267,12940],{},[1156,13269,1158],{},[1156,13271,1247],{"mathvariant":2014},[1172,13273,13274],{"encoding":1174},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,13276,13277],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,13279,13280,1204,13283,2529],{},[1445,13281,13282],{},"Rozptyl",[1445,13284,13285],{},"směrodatná odchylka",[1115,13287,13289],{"className":13288},[1136],[1138,13290,13291],{"xmlns":1140,"display":1897},[1142,13292,13293,13432],{},[1145,13294,13295,13298,13300,13302,13304,13306,13318,13320,13322,13324,13326,13328,13330,13332,13338,13340,13342,13344,13346,13348,13350,13352,13354,13366,13372,13374,13376,13378,13380,13382,13384,13386,13388,13390,13392,13394,13396,13398,13404,13406,13408,13410,13412,13414,13416,13418,13430],{},[1156,13296,13297],{},"D",[1148,13299,1151],{"stretchy":1150},[1156,13301,2168],{},[1148,13303,1170],{"stretchy":1150},[1148,13305,1914],{},[8555,13307,13308,13310,13316],{},[1148,13309,12919],{},[1145,13311,13312,13314],{},[1148,13313,1990],{},[1156,13315,12580],{"mathvariant":2014},[1156,13317,12580],{"mathvariant":2014},[1148,13319,3877],{"stretchy":1150},[1156,13321,1158],{},[1148,13323,1990],{},[1156,13325,13230],{},[1148,13327,1151],{"stretchy":1150},[1156,13329,2168],{},[1148,13331,1170],{"stretchy":1150},[5465,13333,13334,13336],{},[1148,13335,3885],{"stretchy":1150},[1919,13337,2302],{},[1156,13339,11920],{},[1148,13341,1151],{"stretchy":1150},[1156,13343,1158],{},[1148,13345,1170],{"stretchy":1150},[5009,13347,5011],{},[1156,13349,12940],{},[1156,13351,1158],{},[1148,13353,1914],{},[8555,13355,13356,13358,13364],{},[1148,13357,12919],{},[1145,13359,13360,13362],{},[1148,13361,1990],{},[1156,13363,12580],{"mathvariant":2014},[1156,13365,12580],{"mathvariant":2014},[5465,13367,13368,13370],{},[1156,13369,1158],{},[1919,13371,2302],{},[1156,13373,11920],{},[1148,13375,1151],{"stretchy":1150},[1156,13377,1158],{},[1148,13379,1170],{"stretchy":1150},[5009,13381,5011],{},[1156,13383,12940],{},[1156,13385,1158],{},[1148,13387,1990],{},[1148,13389,3877],{"stretchy":1150},[1156,13391,13230],{},[1148,13393,1151],{"stretchy":1150},[1156,13395,2168],{},[1148,13397,1170],{"stretchy":1150},[5465,13399,13400,13402],{},[1148,13401,3885],{"stretchy":1150},[1919,13403,2302],{},[1148,13405,1164],{"separator":1121},[1954,13407],{"width":1956},[1156,13409,1693],{},[1148,13411,1151],{"stretchy":1150},[1156,13413,2168],{},[1148,13415,1170],{"stretchy":1150},[1148,13417,1914],{},[5460,13419,13420],{},[1145,13421,13422,13424,13426,13428],{},[1156,13423,13297],{},[1148,13425,1151],{"stretchy":1150},[1156,13427,2168],{},[1148,13429,1170],{"stretchy":1150},[1156,13431,1247],{"mathvariant":2014},[1172,13433,13434],{"encoding":1174},"D(X) = \\int_{-\\infty}^{\\infty} [x - E(X)]^2 f(x)\\,dx = \\int_{-\\infty}^{\\infty} x^2 f(x)\\,dx - [E(X)]^2, \\qquad \\sigma(X) = \\sqrt{D(X)}.",[1110,13436,13437,13438,13441],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[6613,13439,886],{"className":13440,"dataFsResolvedFilePath":6624,"href":6625},[1531],".)",[1110,13443,13444,13447,13448,13461,13462,13480,13481,13494],{},[1445,13445,13446],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,13449,13451],{"className":13450},[1136],[1138,13452,13453],{"xmlns":1140},[1142,13454,13455,13459],{},[1145,13456,13457],{},[1156,13458,2168],{},[1172,13460,2168],{"encoding":1174}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,13463,13465],{"className":13464},[1136],[1138,13466,13467],{"xmlns":1140},[1142,13468,13469,13477],{},[1145,13470,13471],{},[1217,13472,13473,13475],{},[1156,13474,1158],{},[1156,13476,1110],{},[1172,13478,13479],{"encoding":1174},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,13482,13484],{"className":13483},[1136],[1138,13485,13486],{"xmlns":1140},[1142,13487,13488,13492],{},[1145,13489,13490],{},[1156,13491,1110],{},[1172,13493,1110],{"encoding":1174}," platí",[1115,13496,13498],{"className":13497},[1136],[1138,13499,13500],{"xmlns":1140,"display":1897},[1142,13501,13502,13522],{},[1145,13503,13504,13506,13508,13514,13516,13518,13520],{},[1156,13505,11867],{},[1148,13507,1151],{"stretchy":1150},[1217,13509,13510,13512],{},[1156,13511,1158],{},[1156,13513,1110],{},[1148,13515,1170],{"stretchy":1150},[1148,13517,1914],{},[1156,13519,1110],{},[1156,13521,1247],{"mathvariant":2014},[1172,13523,13524],{"encoding":1174},"F(x_p) = p.",[1110,13526,13527,13528,13556,13557,13584,13585,13604,13605,13624,13625,1247],{},"V intervalu ",[1115,13529,13531],{"className":13530},[1136],[1138,13532,13533],{"xmlns":1140},[1142,13534,13535,13553],{},[1145,13536,13537,13539,13541,13543,13545,13551],{},[1148,13538,1151],{"stretchy":1150},[1148,13540,1990],{},[1156,13542,12580],{"mathvariant":2014},[1148,13544,12041],{"separator":1121},[1217,13546,13547,13549],{},[1156,13548,1158],{},[1156,13550,1110],{},[1148,13552,1170],{"stretchy":1150},[1172,13554,13555],{"encoding":1174},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,13558,13560],{"className":13559},[1136],[1138,13561,13562],{"xmlns":1140},[1142,13563,13564,13581],{},[1145,13565,13566,13569,13575,13577,13579],{},[1148,13567,13568],{"stretchy":1150},"⟨",[1217,13570,13571,13573],{},[1156,13572,1158],{},[1156,13574,1110],{},[1148,13576,12041],{"separator":1121},[1156,13578,12580],{"mathvariant":2014},[1148,13580,1170],{"stretchy":1150},[1172,13582,13583],{"encoding":1174},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,13586,13588],{"className":13587},[1136],[1138,13589,13590],{"xmlns":1140},[1142,13591,13592,13601],{},[1145,13593,13594],{},[1217,13595,13596,13598],{},[1156,13597,1158],{},[1919,13599,13600],{},"0,5",[1172,13602,13603],{"encoding":1174},"x_{0{,}5}",", dolní kvartil ",[1115,13606,13608],{"className":13607},[1136],[1138,13609,13610],{"xmlns":1140},[1142,13611,13612,13621],{},[1145,13613,13614],{},[1217,13615,13616,13618],{},[1156,13617,1158],{},[1919,13619,13620],{},"0,25",[1172,13622,13623],{"encoding":1174},"x_{0{,}25}"," a horní kvartil ",[1115,13626,13628],{"className":13627},[1136],[1138,13629,13630],{"xmlns":1140},[1142,13631,13632,13641],{},[1145,13633,13634],{},[1217,13635,13636,13638],{},[1156,13637,1158],{},[1919,13639,13640],{},"0,75",[1172,13642,13643],{"encoding":1174},"x_{0{,}75}",[1437,13645,12022],{"id":13646},"normální-rozdělení",[1110,13648,13649,13650,13663,13664,6884,13667,13694],{},"Spojitá náhodná veličina ",[1115,13651,13653],{"className":13652},[1136],[1138,13654,13655],{"xmlns":1140},[1142,13656,13657,13661],{},[1145,13658,13659],{},[1156,13660,2168],{},[1172,13662,2168],{"encoding":1174}," má ",[1445,13665,13666],{},"normální rozdělení",[1115,13668,13670],{"className":13669},[1136],[1138,13671,13672],{"xmlns":1140},[1142,13673,13674,13692],{},[1145,13675,13676,13678,13680,13682,13684,13690],{},[1156,13677,12034],{},[1148,13679,1151],{"stretchy":1150},[1156,13681,1677],{},[1148,13683,12041],{"separator":1121},[5465,13685,13686,13688],{},[1156,13687,1693],{},[1919,13689,2302],{},[1148,13691,1170],{"stretchy":1150},[1172,13693,12052],{"encoding":1174},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,13696,13698],{"className":13697},[1136],[1138,13699,13700],{"xmlns":1140,"display":1897},[1142,13701,13702,13854],{},[1145,13703,13704,13706,13708,13710,13712,13714,13731,13768,13770,13772,13774,13776,13778,13780,13782,13798,13810,13846,13848,13850,13852],{},[1156,13705,11920],{},[1148,13707,1151],{"stretchy":1150},[1156,13709,1158],{},[1148,13711,1170],{"stretchy":1150},[1148,13713,1914],{},[1916,13715,13716,13718],{},[1919,13717,1921],{},[1145,13719,13720,13722],{},[1156,13721,1693],{},[5460,13723,13724],{},[1145,13725,13726,13728],{},[1919,13727,2302],{},[1156,13729,13730],{},"π",[5465,13732,13733,13736],{},[1156,13734,13735],{},"e",[1145,13737,13738,13740],{},[1148,13739,1990],{},[1916,13741,13742,13758],{},[1145,13743,13744,13746,13748,13750,13752],{},[1148,13745,1151],{"stretchy":1150},[1156,13747,1158],{},[1148,13749,1990],{},[1156,13751,1677],{},[5465,13753,13754,13756],{},[1148,13755,1170],{"stretchy":1150},[1919,13757,2302],{},[1145,13759,13760,13762],{},[1919,13761,2302],{},[5465,13763,13764,13766],{},[1156,13765,1693],{},[1919,13767,2302],{},[1148,13769,1164],{"separator":1121},[1954,13771],{"width":1956},[1156,13773,11867],{},[1148,13775,1151],{"stretchy":1150},[1156,13777,1158],{},[1148,13779,1170],{"stretchy":1150},[1148,13781,1914],{},[1916,13783,13784,13786],{},[1919,13785,1921],{},[1145,13787,13788,13790],{},[1156,13789,1693],{},[5460,13791,13792],{},[1145,13793,13794,13796],{},[1919,13795,2302],{},[1156,13797,13730],{},[8555,13799,13800,13802,13808],{},[1148,13801,12919],{},[1145,13803,13804,13806],{},[1148,13805,1990],{},[1156,13807,12580],{"mathvariant":2014},[1156,13809,1158],{},[5465,13811,13812,13814],{},[1156,13813,13735],{},[1145,13815,13816,13818],{},[1148,13817,1990],{},[1916,13819,13820,13836],{},[1145,13821,13822,13824,13826,13828,13830],{},[1148,13823,1151],{"stretchy":1150},[1156,13825,12288],{},[1148,13827,1990],{},[1156,13829,1677],{},[5465,13831,13832,13834],{},[1148,13833,1170],{"stretchy":1150},[1919,13835,2302],{},[1145,13837,13838,13840],{},[1919,13839,2302],{},[5465,13841,13842,13844],{},[1156,13843,1693],{},[1919,13845,2302],{},[5009,13847,5011],{},[1156,13849,12940],{},[1156,13851,12288],{},[1148,13853,1164],{"separator":1121},[1172,13855,13856],{"encoding":1174},"f(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}, \\qquad F(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\int_{-\\infty}^{x} e^{-\\frac{(t-\\mu)^2}{2\\sigma^2}}\\,dt,",[1110,13858,13859,13860,1176,13884,1247],{},"přičemž ",[1115,13861,13863],{"className":13862},[1136],[1138,13864,13865],{"xmlns":1140},[1142,13866,13867,13881],{},[1145,13868,13869,13871,13873,13875,13877,13879],{},[1156,13870,13230],{},[1148,13872,1151],{"stretchy":1150},[1156,13874,2168],{},[1148,13876,1170],{"stretchy":1150},[1148,13878,1914],{},[1156,13880,1677],{},[1172,13882,13883],{"encoding":1174},"E(X) = \\mu",[1115,13885,13887],{"className":13886},[1136],[1138,13888,13889],{"xmlns":1140},[1142,13890,13891,13909],{},[1145,13892,13893,13895,13897,13899,13901,13903],{},[1156,13894,13297],{},[1148,13896,1151],{"stretchy":1150},[1156,13898,2168],{},[1148,13900,1170],{"stretchy":1150},[1148,13902,1914],{},[5465,13904,13905,13907],{},[1156,13906,1693],{},[1919,13908,2302],{},[1172,13910,13911],{"encoding":1174},"D(X) = \\sigma^2",[1110,13913,13914],{},[1527,13915],{"alt":13916,"className":13917,"src":13918},"mask-nv-normalni",[1531,1532],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,13920,13921,13922,13925,13926,13939,13940,13959,13960,13976,13977,13990,13991,1247],{},"Křivka hustoty se nazývá ",[1445,13923,13924],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,13927,13929],{"className":13928},[1136],[1138,13930,13931],{"xmlns":1140},[1142,13932,13933,13937],{},[1145,13934,13935],{},[1156,13936,1677],{},[1172,13938,1680],{"encoding":1174},", kde má ",[1115,13941,13943],{"className":13942},[1136],[1138,13944,13945],{"xmlns":1140},[1142,13946,13947,13957],{},[1145,13948,13949,13951,13953,13955],{},[1156,13950,11920],{},[1148,13952,1151],{"stretchy":1150},[1156,13954,1158],{},[1148,13956,1170],{"stretchy":1150},[1172,13958,11949],{"encoding":1174}," globální maximum, a ve vzdálenosti ",[1115,13961,13963],{"className":13962},[1136],[1138,13964,13965],{"xmlns":1140},[1142,13966,13967,13973],{},[1145,13968,13969,13971],{},[1919,13970,2327],{},[1156,13972,1693],{},[1172,13974,13975],{"encoding":1174},"3\\sigma"," od ",[1115,13978,13980],{"className":13979},[1136],[1138,13981,13982],{"xmlns":1140},[1142,13983,13984,13988],{},[1145,13985,13986],{},[1156,13987,1677],{},[1172,13989,1680],{"encoding":1174}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,13992,13994],{"className":13993},[1136],[1138,13995,13996],{"xmlns":1140},[1142,13997,13998,14022],{},[1145,13999,14000,14002,14004,14006,14008,14010,14012,14014,14016,14018,14020],{},[1148,14001,1151],{"stretchy":1150},[1156,14003,1677],{},[1148,14005,1990],{},[1919,14007,2327],{},[1156,14009,1693],{},[1148,14011,12041],{"separator":1121},[1156,14013,1677],{},[1148,14015,5066],{},[1919,14017,2327],{},[1156,14019,1693],{},[1148,14021,1170],{"stretchy":1150},[1172,14023,14024],{"encoding":1174},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,14026,14027,14028,6884,14031,14055,14056,1247],{},"Zvláštní postavení má ",[1445,14029,14030],{},"normované normální rozdělení",[1115,14032,14034],{"className":14033},[1136],[1138,14035,14036],{"xmlns":1140},[1142,14037,14038,14052],{},[1145,14039,14040,14042,14044,14046,14048,14050],{},[1156,14041,12034],{},[1148,14043,1151],{"stretchy":1150},[1919,14045,2780],{},[1148,14047,12041],{"separator":1121},[1919,14049,1921],{},[1148,14051,1170],{"stretchy":1150},[1172,14053,14054],{"encoding":1174},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,14057,14059],{"className":14058},[1136],[1138,14060,14061],{"xmlns":1140},[1142,14062,14063,14084],{},[1145,14064,14065,14068,14070,14072,14074,14076,14078,14080,14082],{},[1156,14066,14067],{},"Z",[1148,14069,1914],{},[1148,14071,1151],{"stretchy":1150},[1156,14073,2168],{},[1148,14075,1990],{},[1156,14077,1677],{},[1148,14079,1170],{"stretchy":1150},[1156,14081,4412],{"mathvariant":2014},[1156,14083,1693],{},[1172,14085,14086],{"encoding":1174},"Z = (X-\\mu)\u002F\\sigma",[14088,14089],"graph-mount",{"spec":14090},"{\"title\":\"Hustota normálního rozdělení N(μ; σ²)\",\"alt\":\"Hustota normálního rozdělení f(x) = 1\u002F(σ√(2π)) krát exp(−(x−μ)²\u002F(2σ²)) s nastavitelnou střední hodnotou μ a směrodatnou odchylkou σ. Se zvyšujícím se σ se křivka zplošťuje a rozšiřuje, se změnou μ se posouvá po ose x.\",\"engine\":\"function-plot\",\"xAxis\":{\"label\":\"x\",\"domain\":[-15,15]},\"yAxis\":{\"label\":\"f(x)\",\"domain\":[0,0.9]},\"params\":[{\"name\":\"mu\",\"label\":\"střední hodnota μ\",\"min\":-3,\"max\":3,\"step\":0.5,\"default\":0},{\"name\":\"s\",\"label\":\"směrodatná odchylka σ\",\"min\":0.5,\"max\":3,\"step\":0.25,\"default\":1}],\"curves\":[{\"fn\":\"(1\u002F(s*sqrt(2*PI)))*exp(-((x-mu)^2)\u002F(2*s^2))\",\"label\":\"f(x) = N(μ; σ²)\",\"color\":\"fp-purple\"}],\"markers\":[{\"x\":\"mu\",\"label\":\"μ\"}]}",[1103,14092,14094,14101],{"className":14093,"dataCallout":11568},[1106,11567],[1110,14095,14097,14100],{"className":14096},[1113],[1115,14098],{"className":14099,"ariaHidden":1121},[1118,11575,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,14102,14103,14104,14131,14132,14135,14136,1176,14138,1204,14140,14142,14143,6884,14146,14159,14160,14186,14187,14190,14191,1247],{},"Zápis ",[1115,14105,14107],{"className":14106},[1136],[1138,14108,14109],{"xmlns":1140},[1142,14110,14111,14129],{},[1145,14112,14113,14115,14117,14119,14121,14127],{},[1156,14114,12034],{},[1148,14116,1151],{"stretchy":1150},[1156,14118,1677],{},[1148,14120,12041],{"separator":1121},[5465,14122,14123,14125],{},[1156,14124,1693],{},[1919,14126,2302],{},[1148,14128,1170],{"stretchy":1150},[1172,14130,12052],{"encoding":1174}," v definici používá ",[1445,14133,14134],{},"rozptyl",". Funkce ",[1434,14137,12056],{},[1434,14139,12059],{},[1434,14141,12062],{}," v R ale jako třetí argument berou ",[1445,14144,14145],{},"směrodatnou odchylku",[1115,14147,14149],{"className":14148},[1136],[1138,14150,14151],{"xmlns":1140},[1142,14152,14153,14157],{},[1145,14154,14155],{},[1156,14156,1693],{},[1172,14158,1696],{"encoding":1174},". Má-li náhodná veličina rozdělení ",[1115,14161,14163],{"className":14162},[1136],[1138,14164,14165],{"xmlns":1140},[1142,14166,14167,14183],{},[1145,14168,14169,14171,14173,14176,14178,14181],{},[1156,14170,12034],{},[1148,14172,1151],{"stretchy":1150},[1919,14174,14175],{},"10",[1148,14177,12041],{"separator":1121},[1919,14179,14180],{},"0,12",[1148,14182,1170],{"stretchy":1150},[1172,14184,14185],{"encoding":1174},"N(10; 0{,}12)",", je ",[1434,14188,14189],{},"sd = sqrt(0.12)",", ne ",[1434,14192,14193],{},"sd = 0.12",[1110,14195,14196],{},"V R:",[3261,14198,14200],{"className":3263,"code":14199,"language":71,"meta":3265,"style":3265},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[1434,14201,14202,14212,14223],{"__ignoreMap":3265},[1115,14203,14204,14206,14208,14210],{"class":3270,"line":10},[1115,14205,12056],{"class":3294},[1115,14207,1151],{"class":3277},[1115,14209,2780],{"class":3312},[1115,14211,3283],{"class":3277},[1115,14213,14214,14216,14218,14221],{"class":3270,"line":27},[1115,14215,12059],{"class":3294},[1115,14217,1151],{"class":3277},[1115,14219,14220],{"class":3312},"1.96",[1115,14222,3283],{"class":3277},[1115,14224,14225,14227,14229,14232],{"class":3270,"line":148},[1115,14226,12062],{"class":3294},[1115,14228,1151],{"class":3277},[1115,14230,14231],{"class":3312},"0.975",[1115,14233,3283],{"class":3277},[3261,14235,14238],{"className":14236,"code":14237,"language":4279,"meta":3265},[4277],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[1434,14239,14237],{"__ignoreMap":3265},[1110,14241,14242,14245,14246,14270,14271,7108,14274,1204,14295,14298],{},[1434,14243,14244],{},"dnorm(0)"," je hodnota hustoty ",[1115,14247,14249],{"className":14248},[1136],[1138,14250,14251],{"xmlns":1140},[1142,14252,14253,14267],{},[1145,14254,14255,14257,14259,14261,14263,14265],{},[1156,14256,12034],{},[1148,14258,1151],{"stretchy":1150},[1919,14260,2780],{},[1148,14262,12041],{"separator":1121},[1919,14264,1921],{},[1148,14266,1170],{"stretchy":1150},[1172,14268,14269],{"encoding":1174},"N(0;1)"," v bodě 0, ",[1434,14272,14273],{},"pnorm(1.96)",[1115,14275,14277],{"className":14276},[1136],[1138,14278,14279],{"xmlns":1140},[1142,14280,14281,14292],{},[1145,14282,14283,14285,14287,14290],{},[1156,14284,11867],{},[1148,14286,1151],{"stretchy":1150},[1919,14288,14289],{},"1,96",[1148,14291,1170],{"stretchy":1150},[1172,14293,14294],{"encoding":1174},"F(1{,}96)",[1434,14296,14297],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,14300,14302,14309],{"className":14301,"dataCallout":2145},[1106,2144],[1110,14303,14305,14308],{"className":14304},[1113],[1115,14306],{"className":14307,"ariaHidden":1121},[1118,2152,1120],"Příklad: Návštěvnost zábavního parku",[1110,14310,14311,14312,14347],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,14313,14315],{"className":14314},[1136],[1138,14316,14317],{"xmlns":1140},[1142,14318,14319,14344],{},[1145,14320,14321,14323,14326,14328,14330,14333,14335,14342],{},[1156,14322,2168],{},[1148,14324,14325],{},"∼",[1156,14327,12034],{},[1148,14329,1151],{"stretchy":1150},[1919,14331,14332],{},"230",[1148,14334,12041],{"separator":1121},[5465,14336,14337,14340],{},[1919,14338,14339],{},"27,5",[1919,14341,2302],{},[1148,14343,1170],{"stretchy":1150},[1172,14345,14346],{"encoding":1174},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,14349,14350],{},[1527,14351],{"alt":14352,"className":14353,"src":14354},"mask-nv-priklad-park",[1531,1532],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3261,14356,14358],{"className":3263,"code":14357,"language":71,"meta":3265,"style":3265},"pnorm(180, mean = 230, sd = 27.5)\n",[1434,14359,14360],{"__ignoreMap":3265},[1115,14361,14362,14364,14366,14369,14371,14373,14375,14378,14380,14382,14384,14387],{"class":3270,"line":10},[1115,14363,12059],{"class":3294},[1115,14365,1151],{"class":3277},[1115,14367,14368],{"class":3312},"180",[1115,14370,1164],{"class":3273},[1115,14372,6104],{"class":3280},[1115,14374,3309],{"class":3273},[1115,14376,14377],{"class":3312}," 230",[1115,14379,1164],{"class":3273},[1115,14381,6012],{"class":3280},[1115,14383,3309],{"class":3273},[1115,14385,14386],{"class":3312}," 27.5",[1115,14388,3283],{"class":3277},[3261,14390,14393],{"className":14391,"code":14392,"language":4279,"meta":3265},[4277],"[1] 0.03451817\n",[1434,14394,14392],{"__ignoreMap":3265},[1110,14396,14397],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,14399,14401,14408],{"className":14400,"dataCallout":2145},[1106,2144],[1110,14402,14404,14407],{"className":14403},[1113],[1115,14405],{"className":14406,"ariaHidden":1121},[1118,2152,1120],"Příklad: Délka výrobku",[1110,14409,14410,14411,14445],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,14412,14414],{"className":14413},[1136],[1138,14415,14416],{"xmlns":1140},[1142,14417,14418,14442],{},[1145,14419,14420,14422,14424,14426,14428,14431,14433,14440],{},[1156,14421,2168],{},[1148,14423,14325],{},[1156,14425,12034],{},[1148,14427,1151],{"stretchy":1150},[1919,14429,14430],{},"42",[1148,14432,12041],{"separator":1121},[5465,14434,14435,14438],{},[1919,14436,14437],{},"1,2",[1919,14439,2302],{},[1148,14441,1170],{"stretchy":1150},[1172,14443,14444],{"encoding":1174},"X \\sim N(42; 1{,}2^2)",". Výrobky s délkou 41 až 43 mm jsou zařazeny do 1. jakostní třídy. Jaké je procento výrobků v 1. jakostní třídě?",[1110,14447,14448],{},[1527,14449],{"alt":14450,"className":14451,"src":14452},"mask-nv-priklad-delka",[1531,1532],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3261,14454,14456],{"className":3263,"code":14455,"language":71,"meta":3265,"style":3265},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[1434,14457,14458],{"__ignoreMap":3265},[1115,14459,14460,14462,14464,14467,14469,14471,14473,14476,14478,14480,14482,14485,14487,14489,14491,14493,14496,14498,14500,14502,14504,14506,14508,14510,14512],{"class":3270,"line":10},[1115,14461,12059],{"class":3294},[1115,14463,1151],{"class":3277},[1115,14465,14466],{"class":3312},"43",[1115,14468,1164],{"class":3273},[1115,14470,6104],{"class":3280},[1115,14472,3309],{"class":3273},[1115,14474,14475],{"class":3312}," 42",[1115,14477,1164],{"class":3273},[1115,14479,6012],{"class":3280},[1115,14481,3309],{"class":3273},[1115,14483,14484],{"class":3312}," 1.2",[1115,14486,6207],{"class":3277},[1115,14488,6343],{"class":3273},[1115,14490,6361],{"class":3294},[1115,14492,1151],{"class":3277},[1115,14494,14495],{"class":3312},"41",[1115,14497,1164],{"class":3273},[1115,14499,6104],{"class":3280},[1115,14501,3309],{"class":3273},[1115,14503,14475],{"class":3312},[1115,14505,1164],{"class":3273},[1115,14507,6012],{"class":3280},[1115,14509,3309],{"class":3273},[1115,14511,14484],{"class":3312},[1115,14513,3283],{"class":3277},[3261,14515,14518],{"className":14516,"code":14517,"language":4279,"meta":3265},[4277],"[1] 0.5953432\n",[1434,14519,14517],{"__ignoreMap":3265},[1110,14521,14522],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,14524,14526,14533],{"className":14525,"dataCallout":2145},[1106,2144],[1110,14527,14529,14532],{"className":14528},[1113],[1115,14530],{"className":14531,"ariaHidden":1121},[1118,2152,1120],"Příklad: Obsah ampulky",[1110,14534,14535,14536,14559,14560,14586],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,14537,14539],{"className":14538},[1136],[1138,14540,14541],{"xmlns":1140},[1142,14542,14543,14557],{},[1145,14544,14545,14547,14549,14551,14553,14555],{},[1156,14546,12034],{},[1148,14548,1151],{"stretchy":1150},[1919,14550,14175],{},[1148,14552,12041],{"separator":1121},[1919,14554,14180],{},[1148,14556,1170],{"stretchy":1150},[1172,14558,14185],{"encoding":1174},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,14561,14563],{"className":14562},[1136],[1138,14564,14565],{"xmlns":1140},[1142,14566,14567,14583],{},[1145,14568,14569,14571,14573,14577,14580],{},[1156,14570,1693],{},[1148,14572,1914],{},[5460,14574,14575],{},[1919,14576,14180],{},[1148,14578,14579],{},"≈",[1919,14581,14582],{},"0,346",[1172,14584,14585],{"encoding":1174},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,14588,14589],{},[1527,14590],{"alt":14591,"className":14592,"src":14593},"mask-nv-priklad-ampulka",[1531,1532],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3261,14595,14597],{"className":3263,"code":14596,"language":71,"meta":3265,"style":3265},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[1434,14598,14599],{"__ignoreMap":3265},[1115,14600,14601,14603,14605,14608,14610,14612,14614,14617,14619,14621,14623,14625,14627,14630],{"class":3270,"line":10},[1115,14602,12059],{"class":3294},[1115,14604,1151],{"class":3277},[1115,14606,14607],{"class":3312},"9.8",[1115,14609,1164],{"class":3273},[1115,14611,6104],{"class":3280},[1115,14613,3309],{"class":3273},[1115,14615,14616],{"class":3312}," 10",[1115,14618,1164],{"class":3273},[1115,14620,6012],{"class":3280},[1115,14622,3309],{"class":3273},[1115,14624,6158],{"class":3294},[1115,14626,1151],{"class":3277},[1115,14628,14629],{"class":3312},"0.12",[1115,14631,6019],{"class":3277},[3261,14633,14636],{"className":14634,"code":14635,"language":4279,"meta":3265},[4277],"[1] 0.2818514\n",[1434,14637,14635],{"__ignoreMap":3265},[1110,14639,14640],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1437,14642,14644],{"id":14643},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,14646,14647,14648,14651,14652,14655,14656,14659,14660,4412,14663,14666,14667,14670],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[1434,14649,14650],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[1434,14653,14654],{},"p*"," distribuční funkce (s ",[1434,14657,14658],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[1434,14661,14662],{},"TRUE",[1434,14664,14665],{},"FALSE",", pro horní chvost) a ",[1434,14668,14669],{},"q*"," kvantilová funkce.",[1459,14672,14673,14779],{},[1462,14674,14675],{},[1465,14676,14677,14680,14726,14752],{},[1468,14678,14679],{},"Rozdělení",[1468,14681,14682,14706,14707],{},[1115,14683,14685],{"className":14684},[1136],[1138,14686,14687],{"xmlns":1140},[1142,14688,14689,14703],{},[1145,14690,14691,14693,14695,14697,14699,14701],{},[1156,14692,5126],{},[1148,14694,1151],{"stretchy":1150},[1156,14696,2168],{},[1148,14698,1914],{},[1156,14700,1234],{},[1148,14702,1170],{"stretchy":1150},[1172,14704,14705],{"encoding":1174},"P(X=k)"," \u002F ",[1115,14708,14710],{"className":14709},[1136],[1138,14711,14712],{"xmlns":1140},[1142,14713,14714,14724],{},[1145,14715,14716,14718,14720,14722],{},[1156,14717,11920],{},[1148,14719,1151],{"stretchy":1150},[1156,14721,1158],{},[1148,14723,1170],{"stretchy":1150},[1172,14725,11949],{"encoding":1174},[1468,14727,14728],{},[1115,14729,14731],{"className":14730},[1136],[1138,14732,14733],{"xmlns":1140},[1142,14734,14735,14749],{},[1145,14736,14737,14739,14741,14743,14745,14747],{},[1156,14738,5126],{},[1148,14740,1151],{"stretchy":1150},[1156,14742,2168],{},[1148,14744,11884],{},[1156,14746,1234],{},[1148,14748,1170],{"stretchy":1150},[1172,14750,14751],{"encoding":1174},"P(X \\le k)",[1468,14753,14754,14755],{},"horní chvost ",[1115,14756,14758],{"className":14757},[1136],[1138,14759,14760],{"xmlns":1140},[1142,14761,14762,14776],{},[1145,14763,14764,14766,14768,14770,14772,14774],{},[1156,14765,5126],{},[1148,14767,1151],{"stretchy":1150},[1156,14769,2168],{},[1148,14771,5755],{},[1156,14773,1234],{},[1148,14775,1170],{"stretchy":1150},[1172,14777,14778],{"encoding":1174},"P(X>k)",[1477,14780,14781,14827,14871,14912,14961],{},[1465,14782,14783,14812,14817,14822],{},[1482,14784,14785,14786],{},"Binomické ",[1115,14787,14789],{"className":14788},[1136],[1138,14790,14791],{"xmlns":1140},[1142,14792,14793,14809],{},[1145,14794,14795,14797,14799,14801,14803,14805,14807],{},[1156,14796,7047],{},[1156,14798,1223],{},[1148,14800,1151],{"stretchy":1150},[1156,14802,1292],{},[1148,14804,1164],{"separator":1121},[1156,14806,1110],{},[1148,14808,1170],{"stretchy":1150},[1172,14810,14811],{"encoding":1174},"Bi(n,p)",[1482,14813,14814],{},[1434,14815,14816],{},"dbinom(k, n, p)",[1482,14818,14819],{},[1434,14820,14821],{},"pbinom(k, n, p)",[1482,14823,14824],{},[1434,14825,14826],{},"pbinom(k, n, p, FALSE)",[1465,14828,14829,14856,14861,14866],{},[1482,14830,14831,14832],{},"Poissonovo ",[1115,14833,14835],{"className":14834},[1136],[1138,14836,14837],{"xmlns":1140},[1142,14838,14839,14853],{},[1145,14840,14841,14843,14846,14848,14851],{},[1156,14842,5126],{},[1156,14844,14845],{},"o",[1148,14847,1151],{"stretchy":1150},[1156,14849,14850],{},"λ",[1148,14852,1170],{"stretchy":1150},[1172,14854,14855],{"encoding":1174},"Po(\\lambda)",[1482,14857,14858],{},[1434,14859,14860],{},"dpois(k, lambda)",[1482,14862,14863],{},[1434,14864,14865],{},"ppois(k, lambda)",[1482,14867,14868],{},[1434,14869,14870],{},"ppois(k, lambda, FALSE)",[1465,14872,14873,14897,14902,14907],{},[1482,14874,14875,14876],{},"Geometrické ",[1115,14877,14879],{"className":14878},[1136],[1138,14880,14881],{"xmlns":1140},[1142,14882,14883,14894],{},[1145,14884,14885,14888,14890,14892],{},[1156,14886,14887],{},"G",[1148,14889,1151],{"stretchy":1150},[1156,14891,1110],{},[1148,14893,1170],{"stretchy":1150},[1172,14895,14896],{"encoding":1174},"G(p)",[1482,14898,14899],{},[1434,14900,14901],{},"dgeom(k, p)",[1482,14903,14904],{},[1434,14905,14906],{},"pgeom(k, p)",[1482,14908,14909],{},[1434,14910,14911],{},"pgeom(k, p, FALSE)",[1465,14913,14914,14946,14951,14956],{},[1482,14915,14916,14917],{},"Hypergeometrické ",[1115,14918,14920],{"className":14919},[1136],[1138,14921,14922],{"xmlns":1140},[1142,14923,14924,14943],{},[1145,14925,14926,14928,14930,14932,14934,14937,14939,14941],{},[1156,14927,6797],{},[1148,14929,1151],{"stretchy":1150},[1156,14931,12034],{},[1148,14933,1164],{"separator":1121},[1156,14935,14936],{},"M",[1148,14938,1164],{"separator":1121},[1156,14940,1292],{},[1148,14942,1170],{"stretchy":1150},[1172,14944,14945],{"encoding":1174},"H(N,M,n)",[1482,14947,14948],{},[1434,14949,14950],{},"dhyper(k, M, N-M, n)",[1482,14952,14953],{},[1434,14954,14955],{},"phyper(k, M, N-M, n)",[1482,14957,14958],{},[1434,14959,14960],{},"phyper(k, M, N-M, n, FALSE)",[1465,14962,14963,14987,14992,14997],{},[1482,14964,14965,14966],{},"Exponenciální ",[1115,14967,14969],{"className":14968},[1136],[1138,14970,14971],{"xmlns":1140},[1142,14972,14973,14984],{},[1145,14974,14975,14977,14979,14982],{},[1156,14976,13230],{},[1148,14978,1151],{"stretchy":1150},[1156,14980,14981],{},"δ",[1148,14983,1170],{"stretchy":1150},[1172,14985,14986],{"encoding":1174},"E(\\delta)",[1482,14988,14989],{},[1434,14990,14991],{},"dexp(k, 1\u002Fdelta)",[1482,14993,14994],{},[1434,14995,14996],{},"pexp(k, 1\u002Fdelta)",[1482,14998,14999],{},[1434,15000,15001],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,15003,15005,15012],{"className":15004,"dataCallout":11568},[1106,11567],[1110,15006,15008,15011],{"className":15007},[1113],[1115,15009],{"className":15010,"ariaHidden":1121},[1118,11575,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,15013,15014,15015,15018,15019,15033,15034,14190,15037,1247],{},"R parametrizuje exponenciální rozdělení intenzitou (",[1434,15016,15017],{},"rate","). Je-li ",[1115,15020,15022],{"className":15021},[1136],[1138,15023,15024],{"xmlns":1140},[1142,15025,15026,15030],{},[1145,15027,15028],{},[1156,15029,14981],{},[1172,15031,15032],{"encoding":1174},"\\delta"," střední doba do události, do R se dosazuje ",[1434,15035,15036],{},"1\u002Fdelta",[1434,15038,15039],{},"delta",[1110,15041,15042,15043,15074,15075,15093],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,15044,15046],{"className":15045},[1136],[1138,15047,15048],{"xmlns":1140},[1142,15049,15050,15071],{},[1145,15051,15052,15054,15056,15058,15060,15062,15064,15066,15069],{},[1156,15053,2168],{},[1148,15055,14325],{},[1156,15057,7047],{},[1156,15059,1223],{},[1148,15061,1151],{"stretchy":1150},[1919,15063,2424],{},[1148,15065,12041],{"separator":1121},[1919,15067,15068],{},"0,95",[1148,15070,1170],{"stretchy":1150},[1172,15072,15073],{"encoding":1174},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,15076,15078],{"className":15077},[1136],[1138,15079,15080],{"xmlns":1140},[1142,15081,15082,15090],{},[1145,15083,15084,15086,15088],{},[1156,15085,14981],{},[1148,15087,1914],{},[1919,15089,2424],{},[1172,15091,15092],{"encoding":1174},"\\delta = 5"," nastane událost do 3 jednotek času):",[3261,15095,15097],{"className":3263,"code":15096,"language":71,"meta":3265,"style":3265},"x \u003C- 0:5\nround(dbinom(x, 5, 0.95), 4)\nround(pbinom(x, 5, 0.95), 4)\n\ndelta \u003C- 5\nround(pexp(3, rate = 1 \u002F delta), 4)\n",[1434,15098,15099,15112,15143,15172,15176,15185],{"__ignoreMap":3265},[1115,15100,15101,15103,15105,15107,15109],{"class":3270,"line":10},[1115,15102,1158],{"class":3280},[1115,15104,3291],{"class":3273},[1115,15106,4166],{"class":3312},[1115,15108,2529],{"class":3273},[1115,15110,15111],{"class":3312},"5\n",[1115,15113,15114,15117,15119,15122,15124,15126,15128,15130,15132,15135,15137,15139,15141],{"class":3270,"line":27},[1115,15115,15116],{"class":3294},"round",[1115,15118,1151],{"class":3277},[1115,15120,15121],{"class":3294},"dbinom",[1115,15123,1151],{"class":3277},[1115,15125,1158],{"class":3280},[1115,15127,1164],{"class":3273},[1115,15129,4161],{"class":3312},[1115,15131,1164],{"class":3273},[1115,15133,15134],{"class":3312}," 0.95",[1115,15136,1170],{"class":3277},[1115,15138,1164],{"class":3273},[1115,15140,4184],{"class":3312},[1115,15142,3283],{"class":3277},[1115,15144,15145,15147,15149,15152,15154,15156,15158,15160,15162,15164,15166,15168,15170],{"class":3270,"line":148},[1115,15146,15116],{"class":3294},[1115,15148,1151],{"class":3277},[1115,15150,15151],{"class":3294},"pbinom",[1115,15153,1151],{"class":3277},[1115,15155,1158],{"class":3280},[1115,15157,1164],{"class":3273},[1115,15159,4161],{"class":3312},[1115,15161,1164],{"class":3273},[1115,15163,15134],{"class":3312},[1115,15165,1170],{"class":3277},[1115,15167,1164],{"class":3273},[1115,15169,4184],{"class":3312},[1115,15171,3283],{"class":3277},[1115,15173,15174],{"class":3270,"line":111},[1115,15175,4237],{"emptyLinePlaceholder":4236},[1115,15177,15178,15180,15182],{"class":3270,"line":96},[1115,15179,15039],{"class":3280},[1115,15181,3291],{"class":3273},[1115,15183,15184],{"class":3312}," 5\n",[1115,15186,15187,15189,15191,15194,15196,15198,15200,15203,15205,15207,15209,15212,15214,15216,15218],{"class":3270,"line":89},[1115,15188,15116],{"class":3294},[1115,15190,1151],{"class":3277},[1115,15192,15193],{"class":3294},"pexp",[1115,15195,1151],{"class":3277},[1115,15197,2327],{"class":3312},[1115,15199,1164],{"class":3273},[1115,15201,15202],{"class":3280}," rate",[1115,15204,3309],{"class":3273},[1115,15206,3882],{"class":3312},[1115,15208,6292],{"class":3273},[1115,15210,15211],{"class":3280}," delta",[1115,15213,1170],{"class":3277},[1115,15215,1164],{"class":3273},[1115,15217,4184],{"class":3312},[1115,15219,3283],{"class":3277},[3261,15221,15224],{"className":15222,"code":15223,"language":4279,"meta":3265},[4277],"[1] 0.0000 0.0000 0.0011 0.0214 0.2036 0.7738\n[1] 0.0000 0.0000 0.0012 0.0226 0.2262 1.0000\n[1] 0.4512\n",[1434,15225,15223],{"__ignoreMap":3265},[1437,15227,15229],{"id":15228},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,15231,15232,15233,15236],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[6613,15234,141],{"className":15235,"dataFsResolvedFilePath":6639,"href":6640},[1531],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,15238,15239,9129,15242,15255],{},[1445,15240,15241],{},"Studentovo rozdělení",[1115,15243,15245],{"className":15244},[1136],[1138,15246,15247],{"xmlns":1140},[1142,15248,15249,15253],{},[1145,15250,15251],{},[1156,15252,1234],{},[1172,15254,1234],{"encoding":1174}," stupni volnosti má hustotu pravděpodobnosti",[1115,15257,15259],{"className":15258},[1136],[1138,15260,15261],{"xmlns":1140,"display":1897},[1142,15262,15263,15358],{},[1145,15264,15265,15267,15269,15271,15273,15275,15307,15345,15347,15349,15351,15353,15356],{},[1156,15266,11920],{},[1148,15268,1151],{"stretchy":1150},[1156,15270,1158],{},[1148,15272,1170],{"stretchy":1150},[1148,15274,1914],{},[1916,15276,15277,15279],{},[1919,15278,1921],{},[1145,15280,15281,15283,15303],{},[1156,15282,7047],{},[1145,15284,15285,15287,15293,15295,15301],{},[1148,15286,1151],{"fence":1121},[1916,15288,15289,15291],{},[1919,15290,1921],{},[1919,15292,2302],{},[1148,15294,1164],{"separator":1121},[1916,15296,15297,15299],{},[1156,15298,1234],{},[1919,15300,2302],{},[1148,15302,1170],{"fence":1121},[5460,15304,15305],{},[1156,15306,1234],{},[5465,15308,15309,15329],{},[1145,15310,15311,15313,15315,15317,15327],{},[1148,15312,1151],{"fence":1121},[1919,15314,1921],{},[1148,15316,5066],{},[1916,15318,15319,15325],{},[5465,15320,15321,15323],{},[1156,15322,1158],{},[1919,15324,2302],{},[1156,15326,1234],{},[1148,15328,1170],{"fence":1121},[1145,15330,15331,15333],{},[1148,15332,1990],{},[1916,15334,15335,15343],{},[1145,15336,15337,15339,15341],{},[1156,15338,1234],{},[1148,15340,5066],{},[1919,15342,1921],{},[1919,15344,2302],{},[1148,15346,1164],{"separator":1121},[1954,15348],{"width":1956},[1156,15350,1158],{},[1148,15352,12164],{},[1156,15354,1167],{"mathvariant":15355},"double-struck",[1148,15357,1164],{"separator":1121},[1172,15359,15360],{"encoding":1174},"f(x) = \\frac{1}{B\\left(\\frac12, \\frac{k}{2}\\right)\\sqrt{k}} \\left(1 + \\frac{x^2}{k}\\right)^{-\\frac{k+1}{2}}, \\qquad x \\in \\mathbb{R},",[1110,15362,9673,15363,15376,15377,15390,15391,15404],{},[1115,15364,15366],{"className":15365},[1136],[1138,15367,15368],{"xmlns":1140},[1142,15369,15370,15374],{},[1145,15371,15372],{},[1156,15373,7047],{},[1172,15375,7047],{"encoding":1174}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,15378,15380],{"className":15379},[1136],[1138,15381,15382],{"xmlns":1140},[1142,15383,15384,15388],{},[1145,15385,15386],{},[1156,15387,1234],{},[1172,15389,1234],{"encoding":1174}," určuje tvar křivky — s rostoucím ",[1115,15392,15394],{"className":15393},[1136],[1138,15395,15396],{"xmlns":1140},[1142,15397,15398,15402],{},[1145,15399,15400],{},[1156,15401,1234],{},[1172,15403,1234],{"encoding":1174}," se rozdělení blíží normálnímu.",[1110,15406,15407,9129,15410,15423],{},[1445,15408,15409],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,15411,15413],{"className":15412},[1136],[1138,15414,15415],{"xmlns":1140},[1142,15416,15417,15421],{},[1145,15418,15419],{},[1156,15420,1234],{},[1172,15422,1234],{"encoding":1174}," stupni volnosti:",[1115,15425,15427],{"className":15426},[1136],[1138,15428,15429],{"xmlns":1140,"display":1897},[1142,15430,15431,15516],{},[1145,15432,15433,15435,15437,15439,15441,15443,15474,15490,15504,15506,15508,15510,15512,15514],{},[1156,15434,11920],{},[1148,15436,1151],{"stretchy":1150},[1156,15438,1158],{},[1148,15440,1170],{"stretchy":1150},[1148,15442,1914],{},[1916,15444,15445,15447],{},[1919,15446,1921],{},[1145,15448,15449,15461,15464,15466,15468,15470,15472],{},[5465,15450,15451,15453],{},[1919,15452,2302],{},[1145,15454,15455,15457,15459],{},[1156,15456,1234],{},[1156,15458,4412],{"mathvariant":2014},[1919,15460,2302],{},[1156,15462,15463],{"mathvariant":2014},"Γ",[1148,15465,1151],{"stretchy":1150},[1156,15467,1234],{},[1156,15469,4412],{"mathvariant":2014},[1919,15471,2302],{},[1148,15473,1170],{"stretchy":1150},[5465,15475,15476,15478],{},[1156,15477,1158],{},[1145,15479,15480,15482,15484,15486,15488],{},[1156,15481,1234],{},[1156,15483,4412],{"mathvariant":2014},[1919,15485,2302],{},[1148,15487,1990],{},[1919,15489,1921],{},[5465,15491,15492,15494],{},[1156,15493,13735],{},[1145,15495,15496,15498,15500,15502],{},[1148,15497,1990],{},[1156,15499,1158],{},[1156,15501,4412],{"mathvariant":2014},[1919,15503,2302],{},[1148,15505,1164],{"separator":1121},[1954,15507],{"width":1956},[1156,15509,1158],{},[1148,15511,5755],{},[1919,15513,2780],{},[1148,15515,1164],{"separator":1121},[1172,15517,15518],{"encoding":1174},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,15520,9673,15521,15535],{},[1115,15522,15524],{"className":15523},[1136],[1138,15525,15526],{"xmlns":1140},[1142,15527,15528,15532],{},[1145,15529,15530],{},[1156,15531,15463],{"mathvariant":2014},[1172,15533,15534],{"encoding":1174},"\\Gamma"," je funkce gama.",[1110,15537,15538,15541,15542,1204,15560,2529],{},[1445,15539,15540],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,15543,15545],{"className":15544},[1136],[1138,15546,15547],{"xmlns":1140},[1142,15548,15549,15557],{},[1145,15550,15551],{},[1217,15552,15553,15555],{},[1156,15554,1234],{},[1919,15556,1921],{},[1172,15558,15559],{"encoding":1174},"k_1",[1115,15561,15563],{"className":15562},[1136],[1138,15564,15565],{"xmlns":1140},[1142,15566,15567,15575],{},[1145,15568,15569],{},[1217,15570,15571,15573],{},[1156,15572,1234],{},[1919,15574,2302],{},[1172,15576,15577],{"encoding":1174},"k_2",[1115,15579,15581],{"className":15580},[1136],[1138,15582,15583],{"xmlns":1140,"display":1897},[1142,15584,15585,15750],{},[1145,15586,15587,15589,15591,15593,15595,15597,15633,15667,15687,15739,15741,15743,15745,15747],{},[1156,15588,11920],{},[1148,15590,1151],{"stretchy":1150},[1156,15592,1158],{},[1148,15594,1170],{"stretchy":1150},[1148,15596,1914],{},[1916,15598,15599,15601],{},[1919,15600,1921],{},[1145,15602,15603,15605],{},[1156,15604,7047],{},[1145,15606,15607,15609,15619,15621,15631],{},[1148,15608,1151],{"fence":1121},[1916,15610,15611,15617],{},[1217,15612,15613,15615],{},[1156,15614,1234],{},[1919,15616,1921],{},[1919,15618,2302],{},[1148,15620,1164],{"separator":1121},[1916,15622,15623,15629],{},[1217,15624,15625,15627],{},[1156,15626,1234],{},[1919,15628,2302],{},[1919,15630,2302],{},[1148,15632,1170],{"fence":1121},[5465,15634,15635,15655],{},[1145,15636,15637,15639,15653],{},[1148,15638,1151],{"fence":1121},[1916,15640,15641,15647],{},[1217,15642,15643,15645],{},[1156,15644,1234],{},[1919,15646,1921],{},[1217,15648,15649,15651],{},[1156,15650,1234],{},[1919,15652,2302],{},[1148,15654,1170],{"fence":1121},[1145,15656,15657,15663,15665],{},[1217,15658,15659,15661],{},[1156,15660,1234],{},[1919,15662,1921],{},[1156,15664,4412],{"mathvariant":2014},[1919,15666,2302],{},[5465,15668,15669,15671],{},[1156,15670,1158],{},[1145,15672,15673,15679,15681,15683,15685],{},[1217,15674,15675,15677],{},[1156,15676,1234],{},[1919,15678,1921],{},[1156,15680,4412],{"mathvariant":2014},[1919,15682,2302],{},[1148,15684,1990],{},[1919,15686,1921],{},[5465,15688,15689,15715],{},[1145,15690,15691,15693,15695,15697,15711,15713],{},[1148,15692,1151],{"fence":1121},[1919,15694,1921],{},[1148,15696,5066],{},[1916,15698,15699,15705],{},[1217,15700,15701,15703],{},[1156,15702,1234],{},[1919,15704,1921],{},[1217,15706,15707,15709],{},[1156,15708,1234],{},[1919,15710,2302],{},[1156,15712,1158],{},[1148,15714,1170],{"fence":1121},[1145,15716,15717,15719],{},[1148,15718,1990],{},[1916,15720,15721,15737],{},[1145,15722,15723,15729,15731],{},[1217,15724,15725,15727],{},[1156,15726,1234],{},[1919,15728,1921],{},[1148,15730,5066],{},[1217,15732,15733,15735],{},[1156,15734,1234],{},[1919,15736,2302],{},[1919,15738,2302],{},[1148,15740,1164],{"separator":1121},[1954,15742],{"width":1956},[1156,15744,1158],{},[1148,15746,5755],{},[1919,15748,15749],{},"0.",[1172,15751,15752],{"encoding":1174},"f(x) = \\frac{1}{B\\left(\\frac{k_1}{2}, \\frac{k_2}{2}\\right)} \\left(\\frac{k_1}{k_2}\\right)^{k_1\u002F2} x^{k_1\u002F2 - 1} \\left(1 + \\frac{k_1}{k_2}x\\right)^{-\\frac{k_1+k_2}{2}}, \\qquad x > 0.",[1110,15754,15755],{},[1527,15756],{"alt":15757,"className":15758,"src":15759},"mask-nv-specialni-rozdeleni",[1531,1532],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[14088,15761],{"spec":15762},"{\"title\":\"Studentovo rozdělení a jeho konvergence k normálnímu rozdělení\",\"alt\":\"Srovnání hustoty standardizovaného normálního rozdělení N(0;1) s hustotou Studentova rozdělení pro k = 1, 2 a 4 stupně volnosti. S rostoucím k se Studentovo rozdělení přibližuje normálnímu — má méně těžké konce a vyšší vrchol.\",\"engine\":\"function-plot\",\"xAxis\":{\"label\":\"x\",\"domain\":[-6,6]},\"yAxis\":{\"label\":\"f(x)\",\"domain\":[0,0.42]},\"params\":[],\"curves\":[{\"fn\":\"exp(-x^2\u002F2)\u002Fsqrt(2*PI)\",\"label\":\"N(0; 1)\",\"color\":\"ink\"},{\"fn\":\"(1\u002FPI)*(1+x^2)^(-1)\",\"label\":\"t, k = 1\",\"color\":\"fp-red\"},{\"fn\":\"(1\u002F(2*sqrt(2)))*(1+x^2\u002F2)^(-1.5)\",\"label\":\"t, k = 2\",\"color\":\"fp-purple\"},{\"fn\":\"(3\u002F8)*(1+x^2\u002F4)^(-2.5)\",\"label\":\"t, k = 4\",\"color\":\"paper-500\"}],\"markers\":[]}",[1110,15764,15765],{},"R funkce pro tato tři rozdělení:",[1459,15767,15768,15782],{},[1462,15769,15770],{},[1465,15771,15772,15774,15777,15779],{},[1468,15773,14679],{},[1468,15775,15776],{},"hustota",[1468,15778,11855],{},[1468,15780,15781],{},"kvantil",[1477,15783,15784,15824,15868],{},[1465,15785,15786,15809,15814,15819],{},[1482,15787,15788,15789],{},"Studentovo ",[1115,15790,15792],{"className":15791},[1136],[1138,15793,15794],{"xmlns":1140},[1142,15795,15796,15806],{},[1145,15797,15798,15800,15802,15804],{},[1156,15799,12288],{},[1148,15801,1151],{"stretchy":1150},[1156,15803,1234],{},[1148,15805,1170],{"stretchy":1150},[1172,15807,15808],{"encoding":1174},"t(k)",[1482,15810,15811],{},[1434,15812,15813],{},"dt(x, df = k)",[1482,15815,15816],{},[1434,15817,15818],{},"pt(x, df = k)",[1482,15820,15821],{},[1434,15822,15823],{},"qt(p, df = k)",[1465,15825,15826,15853,15858,15863],{},[1482,15827,15828,15829],{},"Pearsonovo ",[1115,15830,15832],{"className":15831},[1136],[1138,15833,15834],{"xmlns":1140},[1142,15835,15836,15850],{},[1145,15837,15838,15844,15846,15848],{},[5465,15839,15840,15842],{},[1156,15841,6817],{},[1919,15843,2302],{},[1148,15845,1151],{"stretchy":1150},[1156,15847,1234],{},[1148,15849,1170],{"stretchy":1150},[1172,15851,15852],{"encoding":1174},"\\chi^2(k)",[1482,15854,15855],{},[1434,15856,15857],{},"dchisq(x, df = k)",[1482,15859,15860],{},[1434,15861,15862],{},"pchisq(x, df = k)",[1482,15864,15865],{},[1434,15866,15867],{},"qchisq(p, df = k)",[1465,15869,15870,15905,15910,15915],{},[1482,15871,15872,15873],{},"Fisherovo-Snedecorovo ",[1115,15874,15876],{"className":15875},[1136],[1138,15877,15878],{"xmlns":1140},[1142,15879,15880,15902],{},[1145,15881,15882,15884,15886,15892,15894,15900],{},[1156,15883,11867],{},[1148,15885,1151],{"stretchy":1150},[1217,15887,15888,15890],{},[1156,15889,1234],{},[1919,15891,1921],{},[1148,15893,1164],{"separator":1121},[1217,15895,15896,15898],{},[1156,15897,1234],{},[1919,15899,2302],{},[1148,15901,1170],{"stretchy":1150},[1172,15903,15904],{"encoding":1174},"F(k_1, k_2)",[1482,15906,15907],{},[1434,15908,15909],{},"df(x, df1 = k1, df2 = k2)",[1482,15911,15912],{},[1434,15913,15914],{},"pf(x, df1 = k1, df2 = k2)",[1482,15916,15917],{},[1434,15918,15919],{},"qf(p, df1 = k1, df2 = k2)",[1110,15921,15922],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3261,15924,15926],{"className":3263,"code":15925,"language":71,"meta":3265,"style":3265},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[1434,15927,15928,15949,15969],{"__ignoreMap":3265},[1115,15929,15930,15933,15935,15937,15939,15942,15944,15947],{"class":3270,"line":10},[1115,15931,15932],{"class":3294},"qt",[1115,15934,1151],{"class":3277},[1115,15936,14231],{"class":3312},[1115,15938,1164],{"class":3273},[1115,15940,15941],{"class":3280}," df",[1115,15943,3309],{"class":3273},[1115,15945,15946],{"class":3312}," 9",[1115,15948,3283],{"class":3277},[1115,15950,15951,15954,15956,15959,15961,15963,15965,15967],{"class":3270,"line":27},[1115,15952,15953],{"class":3294},"qchisq",[1115,15955,1151],{"class":3277},[1115,15957,15958],{"class":3312},"0.95",[1115,15960,1164],{"class":3273},[1115,15962,15941],{"class":3280},[1115,15964,3309],{"class":3273},[1115,15966,15946],{"class":3312},[1115,15968,3283],{"class":3277},[1115,15970,15971,15974,15976,15978,15980,15983,15985,15987,15989,15992,15994,15996],{"class":3270,"line":148},[1115,15972,15973],{"class":3294},"qf",[1115,15975,1151],{"class":3277},[1115,15977,15958],{"class":3312},[1115,15979,1164],{"class":3273},[1115,15981,15982],{"class":3280}," df1",[1115,15984,3309],{"class":3273},[1115,15986,4197],{"class":3312},[1115,15988,1164],{"class":3273},[1115,15990,15991],{"class":3280}," df2",[1115,15993,3309],{"class":3273},[1115,15995,14616],{"class":3312},[1115,15997,3283],{"class":3277},[3261,15999,16002],{"className":16000,"code":16001,"language":4279,"meta":3265},[4277],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[1434,16003,16001],{"__ignoreMap":3265},[1437,16005,6378],{"id":6377},[1124,16007,16008,16094,16144],{},[1127,16009,16010,16013,16014,16041,16042,4412,16044,4412,16046,16048,16049,16069,16070,16093],{},[1445,16011,16012],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,16015,16017],{"className":16016},[1136],[1138,16018,16019],{"xmlns":1140},[1142,16020,16021,16039],{},[1145,16022,16023,16025,16027,16029,16031,16037],{},[1156,16024,12034],{},[1148,16026,1151],{"stretchy":1150},[1156,16028,1677],{},[1148,16030,12041],{"separator":1121},[5465,16032,16033,16035],{},[1156,16034,1693],{},[1919,16036,2302],{},[1148,16038,1170],{"stretchy":1150},[1172,16040,12052],{"encoding":1174}," používá rozptyl, ale ",[1434,16043,12056],{},[1434,16045,12059],{},[1434,16047,12062],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,16050,16052],{"className":16051},[1136],[1138,16053,16054],{"xmlns":1140},[1142,16055,16056,16066],{},[1145,16057,16058],{},[5460,16059,16060],{},[5465,16061,16062,16064],{},[1156,16063,1693],{},[1919,16065,2302],{},[1172,16067,16068],{"encoding":1174},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,16071,16073],{"className":16072},[1136],[1138,16074,16075],{"xmlns":1140},[1142,16076,16077,16090],{},[1145,16078,16079,16085,16088],{},[5465,16080,16081,16083],{},[1156,16082,1693],{},[1919,16084,2302],{},[1148,16086,16087],{"mathvariant":2014},"≠",[1919,16089,1921],{},[1172,16091,16092],{"encoding":1174},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1127,16095,16096,16123,16124,16143],{},[1445,16097,16098,16122],{},[1115,16099,16101],{"className":16100},[1136],[1138,16102,16103],{"xmlns":1140},[1142,16104,16105,16119],{},[1145,16106,16107,16109,16111,16113,16115,16117],{},[1156,16108,5126],{},[1148,16110,1151],{"stretchy":1150},[1156,16112,2168],{},[1148,16114,1914],{},[1156,16116,1158],{},[1148,16118,1170],{"stretchy":1150},[1172,16120,16121],{"encoding":1174},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,16125,16127],{"className":16126},[1136],[1138,16128,16129],{"xmlns":1140},[1142,16130,16131,16141],{},[1145,16132,16133,16135,16137,16139],{},[1156,16134,11920],{},[1148,16136,1151],{"stretchy":1150},[1156,16138,1158],{},[1148,16140,1170],{"stretchy":1150},[1172,16142,11949],{"encoding":1174}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1127,16145,16146,6884,16149,16166,16167,16184,16185,16188,16189,1247],{},[1445,16147,16148],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,16150,16152],{"className":16151},[1136],[1138,16153,16154],{"xmlns":1140},[1142,16155,16156,16164],{},[1145,16157,16158],{},[1217,16159,16160,16162],{},[1156,16161,1234],{},[1919,16163,1921],{},[1172,16165,15559],{"encoding":1174}," (čitatel) a ",[1115,16168,16170],{"className":16169},[1136],[1138,16171,16172],{"xmlns":1140},[1142,16173,16174,16182],{},[1145,16175,16176],{},[1217,16177,16178,16180],{},[1156,16179,1234],{},[1919,16181,2302],{},[1172,16183,15577],{"encoding":1174}," (jmenovatel) nejsou zaměnitelné — ",[1434,16186,16187],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[1434,16190,16191],{},"qf(p, df2, df1)",[1437,16193,6607],{"id":6606},[1124,16195,16196,16201,16206,16211,16216,16221,16227],{},[1127,16197,16198],{},[6613,16199,6618],{"className":16200,"dataFsResolvedFilePath":6616,"href":6617},[1531],[1127,16202,16203],{},[6613,16204,886],{"className":16205,"dataFsResolvedFilePath":6624,"href":6625},[1531],[1127,16207,16208],{},[6613,16209,141],{"className":16210,"dataFsResolvedFilePath":6639,"href":6640},[1531],[1127,16212,16213],{},[6613,16214,6648],{"className":16215,"dataFsResolvedFilePath":6646,"href":6647},[1531],[1127,16217,16218],{},[6613,16219,716],{"className":16220,"dataFsResolvedFilePath":6654,"href":6655},[1531],[1127,16222,16223],{},[6613,16224,16226],{"className":16225,"dataFsResolvedFilePath":11786,"href":11787},[1531],"regulacni-diagramy-a-indexy-zpusobilosti",[1127,16228,16229],{},[6613,16230,6663],{"className":16231,"dataFsResolvedFilePath":6661,"href":6662},[1531],[1437,16233,6666],{"id":934},[1110,16235,6669,16236,6674],{},[6671,16237,6673],{},[6697,16239,16240],{},"html 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.sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":3265,"searchDepth":27,"depth":27,"links":16242},[16243,16244,16245,16246,16247,16248,16249,16250,16251,16252],{"id":12110,"depth":27,"text":12111},{"id":12416,"depth":27,"text":12417},{"id":13102,"depth":27,"text":13103},{"id":13211,"depth":27,"text":13212},{"id":13646,"depth":27,"text":12022},{"id":14643,"depth":27,"text":14644},{"id":15228,"depth":27,"text":15229},{"id":6377,"depth":27,"text":6378},{"id":6606,"depth":27,"text":6607},{"id":934,"depth":27,"text":6666},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":11774,"description":3265},[16257,16258,16259],"raw\u002Fmask\u002F01 náhodné veličiny.pdf","raw\u002Fmask\u002F01 náhodné veličiny - návod R.pdf","raw\u002Fmask\u002Fpříklady 01 a 02.docx","topics\u002Fnahodne-veliciny-a-rozdeleni",[23,67,812,332,532,71],"y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs",{"id":16264,"title":11768,"body":16265,"course":23,"courses":6735,"created":6736,"description":3265,"extension":6737,"meta":20997,"navigation":4236,"path":20998,"seo":20999,"sources":21000,"stem":21007,"tags":21008,"type":6748,"updated":6736,"__hash__":21009},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":16266,"toc":20988},[16267,16270,16364,16368,16378,16503,16510,16521,16525,16568,16573,16673,16683,16688,16827,16902,16906,17005,17086,17093,17162,17181,17183,17395,17401,17411,17418,17421,17475,17481,17491,17504,17650,17653,17666,17985,17991,17994,17998,18077,18111,18140,18142,18220,18226,18287,18294,18307,18384,18499,18549,18562,18717,18723,18750,18754,18779,18782,18995,19063,19164,19171,19184,19685,19691,19723,19980,20133,20244,20273,20279,20286,20292,20305,20734,20740,20743,20745,20940,20942,20979,20981,20985],[1099,16268,11768],{"id":16269},"popisná-statistika-a-datové-soubory",[1103,16271,16273,16279],{"className":16272,"dataCallout":1108},[1106,1107],[1110,16274,16276,1122],{"className":16275},[1113],[1115,16277],{"className":16278,"ariaHidden":1121},[1118,1119,1120],[1124,16280,16281,16284,16287,16314,16361],{},[1127,16282,16283],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1127,16285,16286],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1127,16288,16289,16290,1247],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,16291,16293],{"className":16292},[1136],[1138,16294,16295],{"xmlns":1140},[1142,16296,16297,16311],{},[1145,16298,16299,16305,16307,16309],{},[1217,16300,16301,16303],{},[1156,16302,11867],{},[1156,16304,1292],{},[1148,16306,1151],{"stretchy":1150},[1156,16308,1158],{},[1148,16310,1170],{"stretchy":1150},[1172,16312,16313],{"encoding":1174},"F_n(x)",[1127,16315,16316,16317,16360],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,16318,16320],{"className":16319},[1136],[1138,16321,16322],{"xmlns":1140},[1142,16323,16324,16357],{},[1145,16325,16326,16333,16335,16341,16343,16349,16351],{},[1217,16327,16328,16331],{},[1156,16329,16330],{},"I",[1156,16332,1934],{},[1148,16334,1164],{"separator":1121},[1217,16336,16337,16339],{},[1156,16338,14067],{},[1156,16340,1934],{},[1148,16342,1164],{"separator":1121},[1217,16344,16345,16347],{},[1156,16346,11920],{},[1156,16348,1934],{},[1148,16350,1164],{"separator":1121},[1217,16352,16353,16355],{},[1156,16354,1110],{},[1156,16356,1934],{},[1172,16358,16359],{"encoding":1174},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1127,16362,16363],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1437,16365,16367],{"id":16366},"základní-pojmy","Základní pojmy",[1110,16369,16370,16373,16374,16377],{},[6613,16371,6618],{"className":16372,"dataFsResolvedFilePath":6616,"href":6617},[1531]," pracuje s ",[1445,16375,16376],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1124,16379,16380,16386,16410,16416,16490],{},[1127,16381,16382,16385],{},[1445,16383,16384],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1127,16387,16388,16391,16392],{},[1445,16389,16390],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1124,16393,16394,16405],{},[1127,16395,16396,16398,16399,16401,16402,16404],{},[1445,16397,6960],{}," (vyjádřitelné číslem) — dále ",[1445,16400,11844],{}," (spočetně mnoho hodnot) nebo ",[1445,16403,11848],{}," (libovolná hodnota v intervalu);",[1127,16406,16407,16409],{},[1445,16408,6953],{}," (vyjádřitelné slovně).",[1127,16411,16412,16415],{},[1445,16413,16414],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1127,16417,16418,16421,16422,1247],{},[1445,16419,16420],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,16423,16425],{"className":16424},[1136],[1138,16426,16427],{"xmlns":1140},[1142,16428,16429,16487],{},[1145,16430,16431,16433,16435,16437,16440,16442,16444,16447,16449,16452,16454,16456,16459,16461,16464,16466,16468,16470,16472,16474,16476,16478,16480,16482,16485],{},[1148,16432,1151],{"stretchy":1150},[1919,16434,8746],{},[5009,16436,5011],{},[1919,16438,16439],{},"500",[1148,16441,1164],{"separator":1121},[5009,16443,5250],{},[1919,16445,16446],{},"38",[5009,16448,5011],{},[1919,16450,16451],{},"000",[1148,16453,1164],{"separator":1121},[5009,16455,5250],{},[1919,16457,16458],{},"37",[5009,16460,5011],{},[1919,16462,16463],{},"800",[1148,16465,1164],{"separator":1121},[5009,16467,5250],{},[1919,16469,14495],{},[5009,16471,5011],{},[1919,16473,16451],{},[1148,16475,1164],{"separator":1121},[5009,16477,5250],{},[1919,16479,8754],{},[5009,16481,5011],{},[1919,16483,16484],{},"200",[1148,16486,1170],{"stretchy":1150},[1172,16488,16489],{"encoding":1174},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1127,16491,16492,16493,1176,16496,1204,16499,16502],{},"Podle počtu sledovaných znaků rozlišujeme ",[1445,16494,16495],{},"jednorozměrné",[1445,16497,16498],{},"dvourozměrné",[1445,16500,16501],{},"vícerozměrné"," datové soubory.",[1110,16504,16505],{},[1527,16506],{"alt":16507,"className":16508,"src":16509},"mask-ilu-zakladni-soubor-vyber",[1531,1532],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,16511,16512,16513,16516,16517,16520],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1445,16514,16515],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1445,16518,16519],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1437,16522,16524],{"id":16523},"empirické-charakteristiky","Empirické charakteristiky",[1110,16526,16527,16528,16531,16532,16535,16536,16549,16550,16553,16554,16567],{},"Zpracováním datového souboru získáme ",[1445,16529,16530],{},"empirické charakteristiky"," a odhad ",[1445,16533,16534],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,16537,16539],{"className":16538},[1136],[1138,16540,16541],{"xmlns":1140},[1142,16542,16543,16547],{},[1145,16544,16545],{},[1156,16546,2168],{},[1172,16548,2168],{"encoding":1174},". Jde o ",[1445,16551,16552],{},"bodové odhady"," charakteristik ",[1115,16555,16557],{"className":16556},[1136],[1138,16558,16559],{"xmlns":1140},[1142,16560,16561,16565],{},[1145,16562,16563],{},[1156,16564,2168],{},[1172,16566,2168],{"encoding":1174},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,16569,16570],{},[1445,16571,16572],{},"Míry polohy",[1115,16574,16576],{"className":16575},[1136],[1138,16577,16578],{"xmlns":1140,"display":1897},[1142,16579,16580,16670],{},[1145,16581,16582,16588,16590,16596,16610,16616,16618],{},[1153,16583,16584,16586],{"accent":1121},[1156,16585,1158],{},[1148,16587,1161],{},[1148,16589,1914],{},[1916,16591,16592,16594],{},[1919,16593,1921],{},[1156,16595,1292],{},[1925,16597,16598,16600,16608],{},[1148,16599,1929],{},[1145,16601,16602,16604,16606],{},[1156,16603,1223],{},[1148,16605,1914],{},[1919,16607,1921],{},[1156,16609,1292],{},[1217,16611,16612,16614],{},[1156,16613,1158],{},[1156,16615,1223],{},[1954,16617],{"width":1956},[1145,16619,16620,16623,16630,16633,16640,16643,16649,16652,16659,16661,16667],{},[5009,16621,16622],{},"(v",[1153,16624,16625,16627],{"accent":1121},[5009,16626,12274],{},[1148,16628,16629],{},"ˊ",[5009,16631,16632],{},"b",[1153,16634,16635,16637],{"accent":1121},[5009,16636,13735],{},[1148,16638,16639],{},"ˇ",[5009,16641,16642],{},"rov",[1153,16644,16645,16647],{"accent":1121},[5009,16646,12274],{},[1148,16648,16629],{},[5009,16650,16651],{}," pr",[1153,16653,16654,16656],{"accent":1121},[5009,16655,1277],{},[1148,16657,16658],{},"˚",[5009,16660,1379],{},[1153,16662,16663,16665],{"accent":1121},[5009,16664,13735],{},[1148,16666,16639],{},[5009,16668,16669],{},"r)",[1172,16671,16672],{"encoding":1174},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,16674,16675,16676,1204,16679,16682],{},"Dalšími mírami polohy jsou ",[1445,16677,16678],{},"medián",[1445,16680,16681],{},"modus"," (nejčetnější hodnota výběru).",[1110,16684,16685],{},[1445,16686,16687],{},"Míry variability",[1115,16689,16691],{"className":16690},[1136],[1138,16692,16693],{"xmlns":1140,"display":1897},[1142,16694,16695,16824],{},[1145,16696,16697,16703,16705,16717,16759,16761,16763,16765,16767,16775,16777],{},[5465,16698,16699,16701],{},[1156,16700,1198],{},[1919,16702,2302],{},[1148,16704,1914],{},[1916,16706,16707,16709],{},[1919,16708,1921],{},[1145,16710,16711,16713,16715],{},[1156,16712,1292],{},[1148,16714,1990],{},[1919,16716,1921],{},[1145,16718,16719,16721,16735,16743,16745,16747,16757],{},[1148,16720,1151],{"fence":1121},[1925,16722,16723,16725,16733],{},[1148,16724,1929],{},[1145,16726,16727,16729,16731],{},[1156,16728,1223],{},[1148,16730,1914],{},[1919,16732,1921],{},[1156,16734,1292],{},[8555,16736,16737,16739,16741],{},[1156,16738,1158],{},[1156,16740,1223],{},[1919,16742,2302],{},[1148,16744,1990],{},[1156,16746,1292],{},[5465,16748,16749,16755],{},[1153,16750,16751,16753],{"accent":1121},[1156,16752,1158],{},[1148,16754,1161],{},[1919,16756,2302],{},[1148,16758,1170],{"fence":1121},[1148,16760,1164],{"separator":1121},[1954,16762],{"width":1956},[1156,16764,1198],{},[1148,16766,1914],{},[5460,16768,16769],{},[5465,16770,16771,16773],{},[1156,16772,1198],{},[1919,16774,2302],{},[1954,16776],{"width":1956},[1145,16778,16779,16781,16787,16789,16795,16797,16803,16806,16812,16815,16821],{},[5009,16780,16622],{},[1153,16782,16783,16785],{"accent":1121},[5009,16784,12274],{},[1148,16786,16629],{},[5009,16788,16632],{},[1153,16790,16791,16793],{"accent":1121},[5009,16792,13735],{},[1148,16794,16639],{},[5009,16796,16642],{},[1153,16798,16799,16801],{"accent":1121},[5009,16800,12274],{},[1148,16802,16629],{},[5009,16804,16805],{}," rozptyl, sm",[1153,16807,16808,16810],{"accent":1121},[5009,16809,13735],{},[1148,16811,16639],{},[5009,16813,16814],{},"rodatn",[1153,16816,16817,16819],{"accent":1121},[5009,16818,6613],{},[1148,16820,16629],{},[5009,16822,16823],{}," odchylka)",[1172,16825,16826],{"encoding":1174},"s^2 = \\frac{1}{n-1}\\left(\\sum_{i=1}^{n} x_i^2 - n\\bar{x}^2\\right), \\qquad s=\\sqrt{s^2} \\qquad \\text{(výběrový rozptyl, směrodatná odchylka)}",[1115,16828,16830],{"className":16829},[1136],[1138,16831,16832],{"xmlns":1140,"display":1897},[1142,16833,16834,16899],{},[1145,16835,16836,16838,16840,16848,16850,16858,16860],{},[1156,16837,1167],{},[1148,16839,1914],{},[1217,16841,16842,16844,16846],{},[1156,16843,1158],{},[1156,16845,1972],{},[1148,16847,1975],{},[1148,16849,1990],{},[1217,16851,16852,16854,16856],{},[1156,16853,1158],{},[1156,16855,1997],{},[1148,16857,1975],{},[1954,16859],{"width":1956},[1145,16861,16862,16865,16871,16873,16880,16883,16889,16891,16897],{},[5009,16863,16864],{},"(varia",[1153,16866,16867,16869],{"accent":1121},[5009,16868,1262],{},[1148,16870,16639],{},[5009,16872,1292],{},[1153,16874,16875,16878],{"accent":1121},[5009,16876,16877],{},"ı",[1148,16879,16629],{},[5009,16881,16882],{}," rozp",[1153,16884,16885,16887],{"accent":1121},[5009,16886,13735],{},[1148,16888,16639],{},[5009,16890,12288],{},[1153,16892,16893,16895],{"accent":1121},[5009,16894,16877],{},[1148,16896,16629],{},[5009,16898,1170],{},[1172,16900,16901],{"encoding":1174},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,16903,16904],{},[1445,16905,13446],{},[1110,16907,16908,16909,16932,16933,16953,16954,16975,16976,17004],{},"Kvantil ",[1115,16910,16912],{"className":16911},[1136],[1138,16913,16914],{"xmlns":1140},[1142,16915,16916,16929],{},[1145,16917,16918],{},[1217,16919,16920,16927],{},[1153,16921,16922,16924],{"accent":1121},[1156,16923,1158],{},[1148,16925,16926],{},"~",[1156,16928,1110],{},[1172,16930,16931],{"encoding":1174},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,16934,16936],{"className":16935},[1136],[1138,16937,16938],{"xmlns":1140},[1142,16939,16940,16950],{},[1145,16941,16942,16944,16946,16948],{},[1919,16943,5001],{},[1156,16945,1110],{},[5009,16947,5011],{},[1156,16949,5014],{"mathvariant":2014},[1172,16951,16952],{"encoding":1174},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,16955,16957],{"className":16956},[1136],[1138,16958,16959],{"xmlns":1140},[1142,16960,16961,16973],{},[1145,16962,16963],{},[1217,16964,16965,16971],{},[1153,16966,16967,16969],{"accent":1121},[1156,16968,1158],{},[1148,16970,16926],{},[1156,16972,1110],{},[1172,16974,16931],{"encoding":1174},", zbylých ",[1115,16977,16979],{"className":16978},[1136],[1138,16980,16981],{"xmlns":1140},[1142,16982,16983,17001],{},[1145,16984,16985,16987,16989,16991,16993,16995,16997,16999],{},[1919,16986,5001],{},[1148,16988,1151],{"stretchy":1150},[1919,16990,1921],{},[1148,16992,1990],{},[1156,16994,1110],{},[1148,16996,1170],{"stretchy":1150},[5009,16998,5011],{},[1156,17000,5014],{"mathvariant":2014},[1172,17002,17003],{"encoding":1174},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1124,17006,17007,17034],{},[1127,17008,17009,6884,17011,17033],{},[1445,17010,16678],{},[1115,17012,17014],{"className":17013},[1136],[1138,17015,17016],{"xmlns":1140},[1142,17017,17018,17030],{},[1145,17019,17020],{},[1217,17021,17022,17028],{},[1153,17023,17024,17026],{"accent":1121},[1156,17025,1158],{},[1148,17027,16926],{},[1919,17029,13600],{},[1172,17031,17032],{"encoding":1174},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1127,17035,17036,6884,17039,1204,17061,6884,17064,1247],{},[1445,17037,17038],{},"dolní kvartil",[1115,17040,17042],{"className":17041},[1136],[1138,17043,17044],{"xmlns":1140},[1142,17045,17046,17058],{},[1145,17047,17048],{},[1217,17049,17050,17056],{},[1153,17051,17052,17054],{"accent":1121},[1156,17053,1158],{},[1148,17055,16926],{},[1919,17057,13620],{},[1172,17059,17060],{"encoding":1174},"\\tilde{x}_{0{,}25}",[1445,17062,17063],{},"horní kvartil",[1115,17065,17067],{"className":17066},[1136],[1138,17068,17069],{"xmlns":1140},[1142,17070,17071,17083],{},[1145,17072,17073],{},[1217,17074,17075,17081],{},[1153,17076,17077,17079],{"accent":1121},[1156,17078,1158],{},[1148,17080,16926],{},[1919,17082,13640],{},[1172,17084,17085],{"encoding":1174},"\\tilde{x}_{0{,}75}",[1110,17087,17088,17089,17092],{},"Datový soubor se do R zadává buď přímo (",[1434,17090,17091],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3261,17094,17096],{"className":3263,"code":17095,"language":71,"meta":3265,"style":3265},"x \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)   # přímé zadání hodnot\n# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1434,17097,17098,17157],{"__ignoreMap":3265},[1115,17099,17100,17102,17104,17106,17108,17111,17113,17116,17118,17121,17123,17126,17128,17130,17132,17134,17136,17139,17141,17144,17146,17148,17150,17152,17154],{"class":3270,"line":10},[1115,17101,1158],{"class":3280},[1115,17103,3291],{"class":3273},[1115,17105,4142],{"class":3294},[1115,17107,1151],{"class":3277},[1115,17109,17110],{"class":3312},"4.1",[1115,17112,1164],{"class":3273},[1115,17114,17115],{"class":3312}," 4.0",[1115,17117,1164],{"class":3273},[1115,17119,17120],{"class":3312}," 3.8",[1115,17122,1164],{"class":3273},[1115,17124,17125],{"class":3312}," 3.9",[1115,17127,1164],{"class":3273},[1115,17129,17120],{"class":3312},[1115,17131,1164],{"class":3273},[1115,17133,17120],{"class":3312},[1115,17135,1164],{"class":3273},[1115,17137,17138],{"class":3312}," 3.5",[1115,17140,1164],{"class":3273},[1115,17142,17143],{"class":3312}," 3.7",[1115,17145,1164],{"class":3273},[1115,17147,17115],{"class":3312},[1115,17149,1164],{"class":3273},[1115,17151,17115],{"class":3312},[1115,17153,3360],{"class":3277},[1115,17155,17156],{"class":3339},"# přímé zadání hodnot\n",[1115,17158,17159],{"class":3270,"line":27},[1115,17160,17161],{"class":3339},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,17163,17164,17165,17168,17169,17172,17173,17176,17177,17180],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[1434,17166,17167],{},"#",": soubor musí ležet v pracovním adresáři R. ",[1434,17170,17171],{},"read.table()"," vrací datovou tabulku (",[1434,17174,17175],{},"data.frame","), proto ",[1434,17178,17179],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,17182,14196],{},[3261,17184,17186],{"className":3263,"code":17185,"language":71,"meta":3265,"style":3265},"x \u003C- c(11.1, 12.7, 10.8, 13.2, 12.7, 13.4, 12.7, 14.4, 14.7, 14.4)\nlength(x)\nmean(x)\nvar(x)\nsd(x)\nmin(x); max(x); max(x) - min(x)\nquantile(x, 0.5, type = 6)\nquantile(x, 0.25, type = 6)\nquantile(x, 0.75, type = 6)\n",[1434,17187,17188,17245,17256,17267,17278,17289,17325,17349,17372],{"__ignoreMap":3265},[1115,17189,17190,17192,17194,17196,17198,17201,17203,17206,17208,17211,17213,17216,17218,17220,17222,17225,17227,17229,17231,17234,17236,17239,17241,17243],{"class":3270,"line":10},[1115,17191,1158],{"class":3280},[1115,17193,3291],{"class":3273},[1115,17195,4142],{"class":3294},[1115,17197,1151],{"class":3277},[1115,17199,17200],{"class":3312},"11.1",[1115,17202,1164],{"class":3273},[1115,17204,17205],{"class":3312}," 12.7",[1115,17207,1164],{"class":3273},[1115,17209,17210],{"class":3312}," 10.8",[1115,17212,1164],{"class":3273},[1115,17214,17215],{"class":3312}," 13.2",[1115,17217,1164],{"class":3273},[1115,17219,17205],{"class":3312},[1115,17221,1164],{"class":3273},[1115,17223,17224],{"class":3312}," 13.4",[1115,17226,1164],{"class":3273},[1115,17228,17205],{"class":3312},[1115,17230,1164],{"class":3273},[1115,17232,17233],{"class":3312}," 14.4",[1115,17235,1164],{"class":3273},[1115,17237,17238],{"class":3312}," 14.7",[1115,17240,1164],{"class":3273},[1115,17242,17233],{"class":3312},[1115,17244,3283],{"class":3277},[1115,17246,17247,17250,17252,17254],{"class":3270,"line":27},[1115,17248,17249],{"class":3294},"length",[1115,17251,1151],{"class":3277},[1115,17253,1158],{"class":3280},[1115,17255,3283],{"class":3277},[1115,17257,17258,17261,17263,17265],{"class":3270,"line":148},[1115,17259,17260],{"class":3294},"mean",[1115,17262,1151],{"class":3277},[1115,17264,1158],{"class":3280},[1115,17266,3283],{"class":3277},[1115,17268,17269,17272,17274,17276],{"class":3270,"line":111},[1115,17270,17271],{"class":3294},"var",[1115,17273,1151],{"class":3277},[1115,17275,1158],{"class":3280},[1115,17277,3283],{"class":3277},[1115,17279,17280,17283,17285,17287],{"class":3270,"line":96},[1115,17281,17282],{"class":3294},"sd",[1115,17284,1151],{"class":3277},[1115,17286,1158],{"class":3280},[1115,17288,3283],{"class":3277},[1115,17290,17291,17293,17295,17297,17299,17301,17303,17305,17307,17309,17311,17313,17315,17317,17319,17321,17323],{"class":3270,"line":89},[1115,17292,1997],{"class":3294},[1115,17294,1151],{"class":3277},[1115,17296,1158],{"class":3280},[1115,17298,6111],{"class":3277},[1115,17300,1972],{"class":3294},[1115,17302,1151],{"class":3277},[1115,17304,1158],{"class":3280},[1115,17306,6111],{"class":3277},[1115,17308,1972],{"class":3294},[1115,17310,1151],{"class":3277},[1115,17312,1158],{"class":3280},[1115,17314,6207],{"class":3277},[1115,17316,6343],{"class":3273},[1115,17318,6231],{"class":3294},[1115,17320,1151],{"class":3277},[1115,17322,1158],{"class":3280},[1115,17324,3283],{"class":3277},[1115,17326,17327,17330,17332,17334,17336,17339,17341,17343,17345,17347],{"class":3270,"line":82},[1115,17328,17329],{"class":3294},"quantile",[1115,17331,1151],{"class":3277},[1115,17333,1158],{"class":3280},[1115,17335,1164],{"class":3273},[1115,17337,17338],{"class":3312}," 0.5",[1115,17340,1164],{"class":3273},[1115,17342,3328],{"class":3280},[1115,17344,3309],{"class":3273},[1115,17346,4171],{"class":3312},[1115,17348,3283],{"class":3277},[1115,17350,17351,17353,17355,17357,17359,17362,17364,17366,17368,17370],{"class":3270,"line":75},[1115,17352,17329],{"class":3294},[1115,17354,1151],{"class":3277},[1115,17356,1158],{"class":3280},[1115,17358,1164],{"class":3273},[1115,17360,17361],{"class":3312}," 0.25",[1115,17363,1164],{"class":3273},[1115,17365,3328],{"class":3280},[1115,17367,3309],{"class":3273},[1115,17369,4171],{"class":3312},[1115,17371,3283],{"class":3277},[1115,17373,17374,17376,17378,17380,17382,17385,17387,17389,17391,17393],{"class":3270,"line":9071},[1115,17375,17329],{"class":3294},[1115,17377,1151],{"class":3277},[1115,17379,1158],{"class":3280},[1115,17381,1164],{"class":3273},[1115,17383,17384],{"class":3312}," 0.75",[1115,17386,1164],{"class":3273},[1115,17388,3328],{"class":3280},[1115,17390,3309],{"class":3273},[1115,17392,4171],{"class":3312},[1115,17394,3283],{"class":3277},[3261,17396,17399],{"className":17397,"code":17398,"language":4279,"meta":3265},[4277],"[1] 10\n[1] 13.01\n[1] 1.747667\n[1] 1.321993\n[1] 10.8\n[1] 14.7\n[1] 3.9\n  50% \n12.95 \n 25% \n12.3 \n 75% \n14.4 \n",[1434,17400,17398],{"__ignoreMap":3265},[1110,17402,17403,17406,17407,17410],{},[1434,17404,17405],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[1434,17408,17409],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,17412,17413],{},[1527,17414],{"alt":17415,"className":17416,"src":17417},"mask-ps-kvantily",[1531,1532],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,17419,17420],{},"Seřazení souboru a krabicový graf:",[3261,17422,17424],{"className":3263,"code":17423,"language":71,"meta":3265,"style":3265},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[1434,17425,17426,17441,17464],{"__ignoreMap":3265},[1115,17427,17428,17431,17433,17435,17438],{"class":3270,"line":10},[1115,17429,17430],{"class":3294},"sort",[1115,17432,1151],{"class":3277},[1115,17434,1158],{"class":3280},[1115,17436,17437],{"class":3277},")                     ",[1115,17439,17440],{"class":3339},"# vzestupně\n",[1115,17442,17443,17445,17447,17449,17451,17454,17456,17458,17461],{"class":3270,"line":27},[1115,17444,17430],{"class":3294},[1115,17446,1151],{"class":3277},[1115,17448,1158],{"class":3280},[1115,17450,1164],{"class":3273},[1115,17452,17453],{"class":3280}," decreasing",[1115,17455,3309],{"class":3273},[1115,17457,3313],{"class":3312},[1115,17459,17460],{"class":3277},")  ",[1115,17462,17463],{"class":3339},"# sestupně\n",[1115,17465,17466,17469,17471,17473],{"class":3270,"line":148},[1115,17467,17468],{"class":3294},"boxplot",[1115,17470,1151],{"class":3277},[1115,17472,1158],{"class":3280},[1115,17474,3283],{"class":3277},[3261,17476,17479],{"className":17477,"code":17478,"language":4279,"meta":3265},[4277]," [1] 10.8 11.1 12.7 12.7 12.7 13.2 13.4 14.4 14.4 14.7\n [1] 14.7 14.4 14.4 13.4 13.2 12.7 12.7 12.7 11.1 10.8\n",[1434,17480,17478],{"__ignoreMap":3265},[1110,17482,17483,17486,17487,17490],{},[1434,17484,17485],{},"boxplot()"," kreslí krabici mezi hodnotami ",[1434,17488,17489],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,17492,17494,17501],{"className":17493,"dataCallout":2145},[1106,2144],[1110,17495,17497,17500],{"className":17496},[1113],[1115,17498],{"className":17499,"ariaHidden":1121},[1118,2152,1120],"Příklad: Empirické charakteristiky",[1110,17502,17503],{},"Na deseti náhodně vybraných mechanicích byla měřena doba opravy vadné součástky (v minutách):\n11,1  12,7  10,8  13,2  12,7  13,4  12,7  14,4  14,7  14,4.\nUrčete empirické charakteristiky a kvantily.",[1110,17505,17506,17507,1176,17530,1176,17553,1176,17572,17591,17592,13604,17619,17634,17635,1247],{},"Výstup R kódu výše dává ",[1115,17508,17510],{"className":17509},[1136],[1138,17511,17512],{"xmlns":1140},[1142,17513,17514,17527],{},[1145,17515,17516,17522,17524],{},[1153,17517,17518,17520],{"accent":1121},[1156,17519,1158],{},[1148,17521,1161],{},[1148,17523,1914],{},[1919,17525,17526],{},"13,01",[1172,17528,17529],{"encoding":1174},"\\bar{x}=13{,}01",[1115,17531,17533],{"className":17532},[1136],[1138,17534,17535],{"xmlns":1140},[1142,17536,17537,17550],{},[1145,17538,17539,17545,17547],{},[5465,17540,17541,17543],{},[1156,17542,1198],{},[1919,17544,2302],{},[1148,17546,1914],{},[1919,17548,17549],{},"1,75",[1172,17551,17552],{"encoding":1174},"s^2=1{,}75",[1115,17554,17556],{"className":17555},[1136],[1138,17557,17558],{"xmlns":1140},[1142,17559,17560,17569],{},[1145,17561,17562,17564,17566],{},[1156,17563,1198],{},[1148,17565,1914],{},[1919,17567,17568],{},"1,32",[1172,17570,17571],{"encoding":1174},"s=1{,}32",[1115,17573,17575],{"className":17574},[1136],[1138,17576,17577],{"xmlns":1140},[1142,17578,17579,17588],{},[1145,17580,17581,17583,17585],{},[1156,17582,1167],{},[1148,17584,1914],{},[1919,17586,17587],{},"3,9",[1172,17589,17590],{"encoding":1174},"R=3{,}9",", medián ",[1115,17593,17595],{"className":17594},[1136],[1138,17596,17597],{"xmlns":1140},[1142,17598,17599,17616],{},[1145,17600,17601,17611,17613],{},[1217,17602,17603,17609],{},[1153,17604,17605,17607],{"accent":1121},[1156,17606,1158],{},[1148,17608,16926],{},[1919,17610,13600],{},[1148,17612,1914],{},[1919,17614,17615],{},"12,95",[1172,17617,17618],{"encoding":1174},"\\tilde{x}_{0{,}5}=12{,}95",[1115,17620,17622],{"className":17621},[1136],[1138,17623,17624],{"xmlns":1140},[1142,17625,17626,17631],{},[1145,17627,17628],{},[1919,17629,17630],{},"12,3",[1172,17632,17633],{"encoding":1174},"12{,}3",", horní kvartil ",[1115,17636,17638],{"className":17637},[1136],[1138,17639,17640],{"xmlns":1140},[1142,17641,17642,17647],{},[1145,17643,17644],{},[1919,17645,17646],{},"14,4",[1172,17648,17649],{"encoding":1174},"14{,}4",[1110,17651,17652],{},"Odhad střední doby opravy je přibližně 13 minut, odhad směrodatné odchylky přibližně 1,32 minuty. Odchylka je vzhledem k průměru nízká — data kolísají kolem průměru jen málo. Uspořádaný soubor má medián 12,95: polovina oprav trvala méně, polovina více; 25 % oprav bylo kratších než 12,3 minuty a 75 % kratších než 14,4 minuty.",[1103,17654,17656,17663],{"className":17655,"dataCallout":2145},[1106,2144],[1110,17657,17659,17662],{"className":17658},[1113],[1115,17660],{"className":17661,"ariaHidden":1121},[1118,2152,1120],"Příklad: Doba oprav televizorů",[1110,17664,17665],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3261,17667,17669],{"className":3263,"code":17668,"language":71,"meta":3265,"style":3265},"x6 \u003C- c(44, 40.2, 41.9, 43.4, 42.8, 42.3, 43.2, 45, 41.5, 42.7,\n        43.9, 40.1, 43.3, 41.1, 42.5, 42.4, 41.4, 40.8, 42, 44.7,\n        41.2, 41.9, 42.4, 44.4, 40.5, 39.7, 41.1, 41, 41.9, 40.8,\n        43, 42.8, 42.9, 42.7, 43.3, 42.2, 39.2, 41.5, 41.6, 42.7,\n        45, 42.3, 43.6, 43.2, 38.8, 43, 44.2, 43, 40, 44.4)\nlength(x6)\nmean(x6)\nsd(x6)\nmax(x6) - min(x6)\nmedian(x6)\n",[1434,17670,17671,17731,17782,17829,17876,17924,17934,17944,17954,17974],{"__ignoreMap":3265},[1115,17672,17673,17676,17678,17680,17682,17684,17686,17689,17691,17694,17696,17699,17701,17704,17706,17709,17711,17714,17716,17719,17721,17724,17726,17729],{"class":3270,"line":10},[1115,17674,17675],{"class":3280},"x6",[1115,17677,3291],{"class":3273},[1115,17679,4142],{"class":3294},[1115,17681,1151],{"class":3277},[1115,17683,8770],{"class":3312},[1115,17685,1164],{"class":3273},[1115,17687,17688],{"class":3312}," 40.2",[1115,17690,1164],{"class":3273},[1115,17692,17693],{"class":3312}," 41.9",[1115,17695,1164],{"class":3273},[1115,17697,17698],{"class":3312}," 43.4",[1115,17700,1164],{"class":3273},[1115,17702,17703],{"class":3312}," 42.8",[1115,17705,1164],{"class":3273},[1115,17707,17708],{"class":3312}," 42.3",[1115,17710,1164],{"class":3273},[1115,17712,17713],{"class":3312}," 43.2",[1115,17715,1164],{"class":3273},[1115,17717,17718],{"class":3312}," 45",[1115,17720,1164],{"class":3273},[1115,17722,17723],{"class":3312}," 41.5",[1115,17725,1164],{"class":3273},[1115,17727,17728],{"class":3312}," 42.7",[1115,17730,8922],{"class":3273},[1115,17732,17733,17736,17738,17741,17743,17746,17748,17751,17753,17756,17758,17761,17763,17766,17768,17771,17773,17775,17777,17780],{"class":3270,"line":27},[1115,17734,17735],{"class":3312},"        43.9",[1115,17737,1164],{"class":3273},[1115,17739,17740],{"class":3312}," 40.1",[1115,17742,1164],{"class":3273},[1115,17744,17745],{"class":3312}," 43.3",[1115,17747,1164],{"class":3273},[1115,17749,17750],{"class":3312}," 41.1",[1115,17752,1164],{"class":3273},[1115,17754,17755],{"class":3312}," 42.5",[1115,17757,1164],{"class":3273},[1115,17759,17760],{"class":3312}," 42.4",[1115,17762,1164],{"class":3273},[1115,17764,17765],{"class":3312}," 41.4",[1115,17767,1164],{"class":3273},[1115,17769,17770],{"class":3312}," 40.8",[1115,17772,1164],{"class":3273},[1115,17774,14475],{"class":3312},[1115,17776,1164],{"class":3273},[1115,17778,17779],{"class":3312}," 44.7",[1115,17781,8922],{"class":3273},[1115,17783,17784,17787,17789,17791,17793,17795,17797,17800,17802,17805,17807,17810,17812,17814,17816,17819,17821,17823,17825,17827],{"class":3270,"line":148},[1115,17785,17786],{"class":3312},"        41.2",[1115,17788,1164],{"class":3273},[1115,17790,17693],{"class":3312},[1115,17792,1164],{"class":3273},[1115,17794,17760],{"class":3312},[1115,17796,1164],{"class":3273},[1115,17798,17799],{"class":3312}," 44.4",[1115,17801,1164],{"class":3273},[1115,17803,17804],{"class":3312}," 40.5",[1115,17806,1164],{"class":3273},[1115,17808,17809],{"class":3312}," 39.7",[1115,17811,1164],{"class":3273},[1115,17813,17750],{"class":3312},[1115,17815,1164],{"class":3273},[1115,17817,17818],{"class":3312}," 41",[1115,17820,1164],{"class":3273},[1115,17822,17693],{"class":3312},[1115,17824,1164],{"class":3273},[1115,17826,17770],{"class":3312},[1115,17828,8922],{"class":3273},[1115,17830,17831,17834,17836,17838,17840,17843,17845,17847,17849,17851,17853,17856,17858,17861,17863,17865,17867,17870,17872,17874],{"class":3270,"line":111},[1115,17832,17833],{"class":3312},"        43",[1115,17835,1164],{"class":3273},[1115,17837,17703],{"class":3312},[1115,17839,1164],{"class":3273},[1115,17841,17842],{"class":3312}," 42.9",[1115,17844,1164],{"class":3273},[1115,17846,17728],{"class":3312},[1115,17848,1164],{"class":3273},[1115,17850,17745],{"class":3312},[1115,17852,1164],{"class":3273},[1115,17854,17855],{"class":3312}," 42.2",[1115,17857,1164],{"class":3273},[1115,17859,17860],{"class":3312}," 39.2",[1115,17862,1164],{"class":3273},[1115,17864,17723],{"class":3312},[1115,17866,1164],{"class":3273},[1115,17868,17869],{"class":3312}," 41.6",[1115,17871,1164],{"class":3273},[1115,17873,17728],{"class":3312},[1115,17875,8922],{"class":3273},[1115,17877,17878,17881,17883,17885,17887,17890,17892,17894,17896,17899,17901,17904,17906,17909,17911,17913,17915,17918,17920,17922],{"class":3270,"line":96},[1115,17879,17880],{"class":3312},"        45",[1115,17882,1164],{"class":3273},[1115,17884,17708],{"class":3312},[1115,17886,1164],{"class":3273},[1115,17888,17889],{"class":3312}," 43.6",[1115,17891,1164],{"class":3273},[1115,17893,17713],{"class":3312},[1115,17895,1164],{"class":3273},[1115,17897,17898],{"class":3312}," 38.8",[1115,17900,1164],{"class":3273},[1115,17902,17903],{"class":3312}," 43",[1115,17905,1164],{"class":3273},[1115,17907,17908],{"class":3312}," 44.2",[1115,17910,1164],{"class":3273},[1115,17912,17903],{"class":3312},[1115,17914,1164],{"class":3273},[1115,17916,17917],{"class":3312}," 40",[1115,17919,1164],{"class":3273},[1115,17921,17799],{"class":3312},[1115,17923,3283],{"class":3277},[1115,17925,17926,17928,17930,17932],{"class":3270,"line":89},[1115,17927,17249],{"class":3294},[1115,17929,1151],{"class":3277},[1115,17931,17675],{"class":3280},[1115,17933,3283],{"class":3277},[1115,17935,17936,17938,17940,17942],{"class":3270,"line":82},[1115,17937,17260],{"class":3294},[1115,17939,1151],{"class":3277},[1115,17941,17675],{"class":3280},[1115,17943,3283],{"class":3277},[1115,17945,17946,17948,17950,17952],{"class":3270,"line":75},[1115,17947,17282],{"class":3294},[1115,17949,1151],{"class":3277},[1115,17951,17675],{"class":3280},[1115,17953,3283],{"class":3277},[1115,17955,17956,17958,17960,17962,17964,17966,17968,17970,17972],{"class":3270,"line":9071},[1115,17957,1972],{"class":3294},[1115,17959,1151],{"class":3277},[1115,17961,17675],{"class":3280},[1115,17963,6207],{"class":3277},[1115,17965,6343],{"class":3273},[1115,17967,6231],{"class":3294},[1115,17969,1151],{"class":3277},[1115,17971,17675],{"class":3280},[1115,17973,3283],{"class":3277},[1115,17975,17976,17979,17981,17983],{"class":3270,"line":72},[1115,17977,17978],{"class":3294},"median",[1115,17980,1151],{"class":3277},[1115,17982,17675],{"class":3280},[1115,17984,3283],{"class":3277},[3261,17986,17989],{"className":17987,"code":17988,"language":4279,"meta":3265},[4277],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[1434,17990,17988],{"__ignoreMap":3265},[1110,17992,17993],{},"Průměrná doba opravy je 42,27 minuty se směrodatnou odchylkou 1,48 minuty a mediánem 42,4 minuty; průměr a medián téměř splývají, data jsou kolem středu rozložena souměrně.",[1437,17995,17997],{"id":17996},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,17999,18000,18001,18014,18015,6884,18018,18041,18042,18076],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,18002,18004],{"className":18003},[1136],[1138,18005,18006],{"xmlns":1140},[1142,18007,18008,18012],{},[1145,18009,18010],{},[1156,18011,2168],{},[1172,18013,2168],{"encoding":1174},", lze sestrojit ",[1445,18016,18017],{},"empirickou distribuční funkci",[1115,18019,18021],{"className":18020},[1136],[1138,18022,18023],{"xmlns":1140},[1142,18024,18025,18039],{},[1145,18026,18027,18033,18035,18037],{},[1217,18028,18029,18031],{},[1156,18030,11867],{},[1156,18032,1292],{},[1148,18034,1151],{"stretchy":1150},[1156,18036,1158],{},[1148,18038,1170],{"stretchy":1150},[1172,18040,16313],{"encoding":1174},". Pro datový soubor ",[1115,18043,18045],{"className":18044},[1136],[1138,18046,18047],{"xmlns":1140},[1142,18048,18049,18073],{},[1145,18050,18051,18053,18059,18061,18063,18065,18071],{},[1148,18052,1151],{"stretchy":1150},[1217,18054,18055,18057],{},[1156,18056,1158],{},[1919,18058,1921],{},[1148,18060,1164],{"separator":1121},[1148,18062,2043],{},[1148,18064,1164],{"separator":1121},[1217,18066,18067,18069],{},[1156,18068,1158],{},[1156,18070,1292],{},[1148,18072,1170],{"stretchy":1150},[1172,18074,18075],{"encoding":1174},"(x_1,\\dots,x_n)"," je",[1115,18078,18080],{"className":18079},[1136],[1138,18081,18082],{"xmlns":1140,"display":1897},[1142,18083,18084,18108],{},[1145,18085,18086,18092,18094,18096,18098,18100,18106],{},[1217,18087,18088,18090],{},[1156,18089,11867],{},[1156,18091,1292],{},[1148,18093,1151],{"stretchy":1150},[1156,18095,1158],{},[1148,18097,1170],{"stretchy":1150},[1148,18099,1914],{},[1916,18101,18102,18104],{},[1156,18103,1234],{},[1156,18105,1292],{},[1148,18107,1164],{"separator":1121},[1172,18109,18110],{"encoding":1174},"F_n(x) = \\frac{k}{n},",[1110,18112,9673,18113,18126,18127,1247],{},[1115,18114,18116],{"className":18115},[1136],[1138,18117,18118],{"xmlns":1140},[1142,18119,18120,18124],{},[1145,18121,18122],{},[1156,18123,1234],{},[1172,18125,1234],{"encoding":1174}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,18128,18130],{"className":18129},[1136],[1138,18131,18132],{"xmlns":1140},[1142,18133,18134,18138],{},[1145,18135,18136],{},[1156,18137,1158],{},[1172,18139,1158],{"encoding":1174},[1110,18141,14196],{},[3261,18143,18145],{"className":3263,"code":18144,"language":71,"meta":3265,"style":3265},"f \u003C- ecdf(x)\nknots(f)        # vzestupně seřazené různé hodnoty datového souboru\nf(knots(f))      # hodnoty Fn(x) v těchto bodech\nf(13)            # Fn v libovolném bodě\nplot(f)\n",[1434,18146,18147,18162,18177,18195,18209],{"__ignoreMap":3265},[1115,18148,18149,18151,18153,18156,18158,18160],{"class":3270,"line":10},[1115,18150,11920],{"class":3280},[1115,18152,3291],{"class":3273},[1115,18154,18155],{"class":3294}," ecdf",[1115,18157,1151],{"class":3277},[1115,18159,1158],{"class":3280},[1115,18161,3283],{"class":3277},[1115,18163,18164,18167,18169,18171,18174],{"class":3270,"line":27},[1115,18165,18166],{"class":3294},"knots",[1115,18168,1151],{"class":3277},[1115,18170,11920],{"class":3280},[1115,18172,18173],{"class":3277},")        ",[1115,18175,18176],{"class":3339},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,18178,18179,18181,18183,18185,18187,18189,18192],{"class":3270,"line":148},[1115,18180,11920],{"class":3294},[1115,18182,1151],{"class":3277},[1115,18184,18166],{"class":3294},[1115,18186,1151],{"class":3277},[1115,18188,11920],{"class":3280},[1115,18190,18191],{"class":3277},"))      ",[1115,18193,18194],{"class":3339},"# hodnoty Fn(x) v těchto bodech\n",[1115,18196,18197,18199,18201,18203,18206],{"class":3270,"line":111},[1115,18198,11920],{"class":3294},[1115,18200,1151],{"class":3277},[1115,18202,2671],{"class":3312},[1115,18204,18205],{"class":3277},")            ",[1115,18207,18208],{"class":3339},"# Fn v libovolném bodě\n",[1115,18210,18211,18214,18216,18218],{"class":3270,"line":96},[1115,18212,18213],{"class":3294},"plot",[1115,18215,1151],{"class":3277},[1115,18217,11920],{"class":3280},[1115,18219,3283],{"class":3277},[3261,18221,18224],{"className":18222,"code":18223,"language":4279,"meta":3265},[4277],"[1] 10.8 11.1 12.7 13.2 13.4 14.4 14.7\n[1] 0.1 0.2 0.5 0.6 0.7 0.9 1.0\n[1] 0.5\n",[1434,18225,18223],{"__ignoreMap":3265},[1110,18227,18228,18231,18232,18250,18251,18254,18255,18268,18269,1247],{},[1434,18229,18230],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,18233,18235],{"className":18234},[1136],[1138,18236,18237],{"xmlns":1140},[1142,18238,18239,18247],{},[1145,18240,18241],{},[1217,18242,18243,18245],{},[1156,18244,11867],{},[1156,18246,1292],{},[1172,18248,18249],{"encoding":1174},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[1434,18252,18253],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,18256,18258],{"className":18257},[1136],[1138,18259,18260],{"xmlns":1140},[1142,18261,18262,18266],{},[1145,18263,18264],{},[1156,18265,1234],{},[1172,18267,1234],{"encoding":1174},"-násobek ",[1115,18270,18272],{"className":18271},[1136],[1138,18273,18274],{"xmlns":1140},[1142,18275,18276,18284],{},[1145,18277,18278,18280,18282],{},[1919,18279,1921],{},[1156,18281,4412],{"mathvariant":2014},[1156,18283,1292],{},[1172,18285,18286],{"encoding":1174},"1\u002Fn",[1110,18288,18289],{},[1527,18290],{"alt":18291,"className":18292,"src":18293},"mask-ps-ecdf",[1531,1532],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,18295,18297,18304],{"className":18296,"dataCallout":2145},[1106,2144],[1110,18298,18300,18303],{"className":18299},[1113],[1115,18301],{"className":18302,"ariaHidden":1121},[1118,2152,1120],"Příklad: Empirická distribuční funkce",[1110,18305,18306],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,18308,18309,18310,1247],{},"Uspořádaný soubor je ",[1115,18311,18313],{"className":18312},[1136],[1138,18314,18315],{"xmlns":1140},[1142,18316,18317,18381],{},[1145,18318,18319,18322,18324,18326,18329,18331,18333,18336,18338,18340,18342,18344,18346,18348,18350,18352,18355,18357,18359,18362,18364,18366,18368,18370,18372,18374,18376,18378],{},[1919,18320,18321],{},"10,8",[1148,18323,12041],{"separator":1121},[5009,18325,5250],{},[1919,18327,18328],{},"11,1",[1148,18330,12041],{"separator":1121},[5009,18332,5250],{},[1919,18334,18335],{},"12,7",[1148,18337,12041],{"separator":1121},[5009,18339,5250],{},[1919,18341,18335],{},[1148,18343,12041],{"separator":1121},[5009,18345,5250],{},[1919,18347,18335],{},[1148,18349,12041],{"separator":1121},[5009,18351,5250],{},[1919,18353,18354],{},"13,2",[1148,18356,12041],{"separator":1121},[5009,18358,5250],{},[1919,18360,18361],{},"13,4",[1148,18363,12041],{"separator":1121},[5009,18365,5250],{},[1919,18367,17646],{},[1148,18369,12041],{"separator":1121},[5009,18371,5250],{},[1919,18373,17646],{},[1148,18375,12041],{"separator":1121},[5009,18377,5250],{},[1919,18379,18380],{},"14,7",[1172,18382,18383],{"encoding":1174},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1459,18385,18386,18419],{},[1462,18387,18388],{},[1465,18389,18390,18405,18407,18409,18411,18413,18415,18417],{},[1468,18391,18392],{},[1115,18393,18395],{"className":18394},[1136],[1138,18396,18397],{"xmlns":1140},[1142,18398,18399,18403],{},[1145,18400,18401],{},[1156,18402,1158],{},[1172,18404,1158],{"encoding":1174},[1468,18406,18321],{},[1468,18408,18328],{},[1468,18410,18335],{},[1468,18412,18354],{},[1468,18414,18361],{},[1468,18416,17646],{},[1468,18418,18380],{},[1477,18420,18421,18452],{},[1465,18422,18423,18438,18440,18442,18444,18446,18448,18450],{},[1482,18424,18425],{},[1115,18426,18428],{"className":18427},[1136],[1138,18429,18430],{"xmlns":1140},[1142,18431,18432,18436],{},[1145,18433,18434],{},[1156,18435,1234],{},[1172,18437,1234],{"encoding":1174},[1482,18439,1921],{},[1482,18441,2302],{},[1482,18443,2424],{},[1482,18445,2437],{},[1482,18447,4147],{},[1482,18449,8789],{},[1482,18451,14175],{},[1465,18453,18454,18479,18482,18485,18487,18490,18493,18496],{},[1482,18455,18456],{},[1115,18457,18459],{"className":18458},[1136],[1138,18460,18461],{"xmlns":1140},[1142,18462,18463,18477],{},[1145,18464,18465,18471,18473,18475],{},[1217,18466,18467,18469],{},[1156,18468,11867],{},[1156,18470,1292],{},[1148,18472,1151],{"stretchy":1150},[1156,18474,1158],{},[1148,18476,1170],{"stretchy":1150},[1172,18478,16313],{"encoding":1174},[1482,18480,18481],{},"0,1",[1482,18483,18484],{},"0,2",[1482,18486,13600],{},[1482,18488,18489],{},"0,6",[1482,18491,18492],{},"0,7",[1482,18494,18495],{},"0,9",[1482,18497,18498],{},"1,0",[1110,18500,18501,18502,18524,18525,18548],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,18503,18505],{"className":18504},[1136],[1138,18506,18507],{"xmlns":1140},[1142,18508,18509,18521],{},[1145,18510,18511,18513,18515,18517,18519],{},[1919,18512,1921],{},[1156,18514,4412],{"mathvariant":2014},[1156,18516,1292],{},[1148,18518,1914],{},[1919,18520,18481],{},[1172,18522,18523],{"encoding":1174},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,18526,18528],{"className":18527},[1136],[1138,18529,18530],{"xmlns":1140},[1142,18531,18532,18545],{},[1145,18533,18534,18536,18538,18540,18542],{},[1919,18535,2327],{},[1156,18537,4412],{"mathvariant":2014},[1156,18539,1292],{},[1148,18541,1914],{},[1919,18543,18544],{},"0,3",[1172,18546,18547],{"encoding":1174},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,18550,18552,18559],{"className":18551,"dataCallout":2145},[1106,2144],[1110,18553,18555,18558],{"className":18554},[1113],[1115,18556],{"className":18557,"ariaHidden":1121},[1118,2152,1120],"Příklad: Odpad materiálu",[1110,18560,18561],{},"Na deseti obráběných kusech byly naměřeny hodnoty odpadu materiálu (v %):\n4,1  4,0  3,8  3,9  3,8  3,8  3,5  3,7  4,0  4,0.\nUrčete empirické charakteristiky a nakreslete empirickou distribuční funkci.",[3261,18563,18565],{"className":3263,"code":18564,"language":71,"meta":3265,"style":3265},"x4 \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)\nlength(x4)\nmean(x4)\nsd(x4)\nmax(x4) - min(x4)\nmedian(x4)\nf4 \u003C- ecdf(x4)\nknots(f4)\nf4(knots(f4))\n",[1434,18566,18567,18618,18628,18638,18648,18668,18678,18693,18703],{"__ignoreMap":3265},[1115,18568,18569,18572,18574,18576,18578,18580,18582,18584,18586,18588,18590,18592,18594,18596,18598,18600,18602,18604,18606,18608,18610,18612,18614,18616],{"class":3270,"line":10},[1115,18570,18571],{"class":3280},"x4",[1115,18573,3291],{"class":3273},[1115,18575,4142],{"class":3294},[1115,18577,1151],{"class":3277},[1115,18579,17110],{"class":3312},[1115,18581,1164],{"class":3273},[1115,18583,17115],{"class":3312},[1115,18585,1164],{"class":3273},[1115,18587,17120],{"class":3312},[1115,18589,1164],{"class":3273},[1115,18591,17125],{"class":3312},[1115,18593,1164],{"class":3273},[1115,18595,17120],{"class":3312},[1115,18597,1164],{"class":3273},[1115,18599,17120],{"class":3312},[1115,18601,1164],{"class":3273},[1115,18603,17138],{"class":3312},[1115,18605,1164],{"class":3273},[1115,18607,17143],{"class":3312},[1115,18609,1164],{"class":3273},[1115,18611,17115],{"class":3312},[1115,18613,1164],{"class":3273},[1115,18615,17115],{"class":3312},[1115,18617,3283],{"class":3277},[1115,18619,18620,18622,18624,18626],{"class":3270,"line":27},[1115,18621,17249],{"class":3294},[1115,18623,1151],{"class":3277},[1115,18625,18571],{"class":3280},[1115,18627,3283],{"class":3277},[1115,18629,18630,18632,18634,18636],{"class":3270,"line":148},[1115,18631,17260],{"class":3294},[1115,18633,1151],{"class":3277},[1115,18635,18571],{"class":3280},[1115,18637,3283],{"class":3277},[1115,18639,18640,18642,18644,18646],{"class":3270,"line":111},[1115,18641,17282],{"class":3294},[1115,18643,1151],{"class":3277},[1115,18645,18571],{"class":3280},[1115,18647,3283],{"class":3277},[1115,18649,18650,18652,18654,18656,18658,18660,18662,18664,18666],{"class":3270,"line":96},[1115,18651,1972],{"class":3294},[1115,18653,1151],{"class":3277},[1115,18655,18571],{"class":3280},[1115,18657,6207],{"class":3277},[1115,18659,6343],{"class":3273},[1115,18661,6231],{"class":3294},[1115,18663,1151],{"class":3277},[1115,18665,18571],{"class":3280},[1115,18667,3283],{"class":3277},[1115,18669,18670,18672,18674,18676],{"class":3270,"line":89},[1115,18671,17978],{"class":3294},[1115,18673,1151],{"class":3277},[1115,18675,18571],{"class":3280},[1115,18677,3283],{"class":3277},[1115,18679,18680,18683,18685,18687,18689,18691],{"class":3270,"line":82},[1115,18681,18682],{"class":3280},"f4",[1115,18684,3291],{"class":3273},[1115,18686,18155],{"class":3294},[1115,18688,1151],{"class":3277},[1115,18690,18571],{"class":3280},[1115,18692,3283],{"class":3277},[1115,18694,18695,18697,18699,18701],{"class":3270,"line":75},[1115,18696,18166],{"class":3294},[1115,18698,1151],{"class":3277},[1115,18700,18682],{"class":3280},[1115,18702,3283],{"class":3277},[1115,18704,18705,18707,18709,18711,18713,18715],{"class":3270,"line":9071},[1115,18706,18682],{"class":3294},[1115,18708,1151],{"class":3277},[1115,18710,18166],{"class":3294},[1115,18712,1151],{"class":3277},[1115,18714,18682],{"class":3280},[1115,18716,6019],{"class":3277},[3261,18718,18721],{"className":18719,"code":18720,"language":4279,"meta":3265},[4277],"[1] 10\n[1] 3.86\n[1] 0.1776388\n[1] 0.6\n[1] 3.85\n[1] 3.5 3.7 3.8 3.9 4.0 4.1\n[1] 0.1 0.2 0.5 0.6 0.9 1.0\n",[1434,18722,18720],{"__ignoreMap":3265},[1110,18724,18725,18726,18749],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,18727,18729],{"className":18728},[1136],[1138,18730,18731],{"xmlns":1140},[1142,18732,18733,18747],{},[1145,18734,18735,18741,18743,18745],{},[1217,18736,18737,18739],{},[1156,18738,11867],{},[1156,18740,1292],{},[1148,18742,1151],{"stretchy":1150},[1156,18744,1158],{},[1148,18746,1170],{"stretchy":1150},[1172,18748,16313],{"encoding":1174},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1437,18751,18753],{"id":18752},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,18755,18756,18757,18760,18761,18774,18775,18778],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1445,18758,18759],{},"roztřídí",": variační rozpětí ",[1115,18762,18764],{"className":18763},[1136],[1138,18765,18766],{"xmlns":1140},[1142,18767,18768,18772],{},[1145,18769,18770],{},[1156,18771,1167],{},[1172,18773,1167],{"encoding":1174}," se rozdělí na určitý počet ",[1445,18776,18777],{},"tříd"," (intervalů) a zjistí se, kolik hodnot do které třídy padne. Na počet ani šířku tříd neexistuje obecný předpis — počet by neměl být ani příliš malý, ani příliš velký.",[1110,18780,18781],{},"Výsledkem je tabulka četností se sloupci:",[1124,18783,18784,18864,18885,18906],{},[1127,18785,18786,18804,18805,18818,18819,18863],{},[1115,18787,18789],{"className":18788},[1136],[1138,18790,18791],{"xmlns":1140},[1142,18792,18793,18801],{},[1145,18794,18795],{},[1217,18796,18797,18799],{},[1156,18798,16330],{},[1156,18800,1934],{},[1172,18802,18803],{"encoding":1174},"I_j"," — ",[1115,18806,18808],{"className":18807},[1136],[1138,18809,18810],{"xmlns":1140},[1142,18811,18812,18816],{},[1145,18813,18814],{},[1156,18815,1934],{},[1172,18817,1934],{"encoding":1174},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,18820,18822],{"className":18821},[1136],[1138,18823,18824],{"xmlns":1140},[1142,18825,18826,18860],{},[1145,18827,18828,18834,18836,18838,18844,18846,18858],{},[1217,18829,18830,18832],{},[1156,18831,16330],{},[1156,18833,1934],{},[1148,18835,1914],{},[1148,18837,13568],{"stretchy":1150},[1217,18839,18840,18842],{},[1156,18841,1262],{},[1156,18843,1934],{},[1148,18845,12041],{"separator":1121},[1217,18847,18848,18850],{},[1156,18849,1262],{},[1145,18851,18852,18854,18856],{},[1156,18853,1934],{},[1148,18855,5066],{},[1919,18857,1921],{},[1148,18859,1170],{"stretchy":1150},[1172,18861,18862],{"encoding":1174},"I_j = \\langle c_j; c_{j+1})","),",[1127,18865,18866,18884],{},[1115,18867,18869],{"className":18868},[1136],[1138,18870,18871],{"xmlns":1140},[1142,18872,18873,18881],{},[1145,18874,18875],{},[1217,18876,18877,18879],{},[1156,18878,14067],{},[1156,18880,1934],{},[1172,18882,18883],{"encoding":1174},"Z_j"," — střed (reprezentant) intervalu,",[1127,18886,18887,18905],{},[1115,18888,18890],{"className":18889},[1136],[1138,18891,18892],{"xmlns":1140},[1142,18893,18894,18902],{},[1145,18895,18896],{},[1217,18897,18898,18900],{},[1156,18899,11920],{},[1156,18901,1934],{},[1172,18903,18904],{"encoding":1174},"f_j"," — četnost, počet hodnot v intervalu,",[1127,18907,18908,18938,18939,1204,18967,1247],{},[1115,18909,18911],{"className":18910},[1136],[1138,18912,18913],{"xmlns":1140},[1142,18914,18915,18935],{},[1145,18916,18917,18923,18925,18931,18933],{},[1217,18918,18919,18921],{},[1156,18920,1110],{},[1156,18922,1934],{},[1148,18924,1914],{},[1217,18926,18927,18929],{},[1156,18928,11920],{},[1156,18930,1934],{},[1156,18932,4412],{"mathvariant":2014},[1156,18934,1292],{},[1172,18936,18937],{"encoding":1174},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,18940,18942],{"className":18941},[1136],[1138,18943,18944],{"xmlns":1140},[1142,18945,18946,18964],{},[1145,18947,18948,18954,18960,18962],{},[1217,18949,18950,18952],{},[1148,18951,1929],{},[1156,18953,1934],{},[1217,18955,18956,18958],{},[1156,18957,11920],{},[1156,18959,1934],{},[1148,18961,1914],{},[1156,18963,1292],{},[1172,18965,18966],{"encoding":1174},"\\sum_j f_j = n",[1115,18968,18970],{"className":18969},[1136],[1138,18971,18972],{"xmlns":1140},[1142,18973,18974,18992],{},[1145,18975,18976,18982,18988,18990],{},[1217,18977,18978,18980],{},[1148,18979,1929],{},[1156,18981,1934],{},[1217,18983,18984,18986],{},[1156,18985,1110],{},[1156,18987,1934],{},[1148,18989,1914],{},[1919,18991,1921],{},[1172,18993,18994],{"encoding":1174},"\\sum_j p_j = 1",[1110,18996,18997,18998,19001,19002,19005,19006,19009,19010,19013,19014,6173,19017,19034,19035,19038,19039,6173,19042,7035,19059,19062],{},"V R se třídění provádí příkazem ",[1434,18999,19000],{},"hist()"," — buď necháme R zvolit třídy samo (",[1434,19003,19004],{},"hist(x)","), nebo zadáme hranice přímo (",[1434,19007,19008],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[1434,19011,19012],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[1434,19015,19016],{},"y$counts",[1115,19018,19020],{"className":19019},[1136],[1138,19021,19022],{"xmlns":1140},[1142,19023,19024,19032],{},[1145,19025,19026],{},[1217,19027,19028,19030],{},[1156,19029,11920],{},[1156,19031,1934],{},[1172,19033,18904],{"encoding":1174},"), ",[1434,19036,19037],{},"y$breaks"," (hranice tříd), ",[1434,19040,19041],{},"y$mids",[1115,19043,19045],{"className":19044},[1136],[1138,19046,19047],{"xmlns":1140},[1142,19048,19049,19057],{},[1145,19050,19051],{},[1217,19052,19053,19055],{},[1156,19054,14067],{},[1156,19056,1934],{},[1172,19058,18883],{"encoding":1174},[1434,19060,19061],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,19064,19065,19066,19083,19084,19086,19087,19123,19124,19127,19128,1247],{},"Interval ",[1115,19067,19069],{"className":19068},[1136],[1138,19070,19071],{"xmlns":1140},[1142,19072,19073,19081],{},[1145,19074,19075],{},[1217,19076,19077,19079],{},[1156,19078,16330],{},[1156,19080,1934],{},[1172,19082,18803],{"encoding":1174}," je ve výchozím nastavení ",[1434,19085,19000],{}," zleva otevřený a zprava uzavřený, ",[1115,19088,19090],{"className":19089},[1136],[1138,19091,19092],{"xmlns":1140},[1142,19093,19094,19120],{},[1145,19095,19096,19098,19104,19106,19118],{},[1148,19097,1151],{"stretchy":1150},[1217,19099,19100,19102],{},[1156,19101,1262],{},[1156,19103,1934],{},[1148,19105,12041],{"separator":1121},[1217,19107,19108,19110],{},[1156,19109,1262],{},[1145,19111,19112,19114,19116],{},[1156,19113,1934],{},[1148,19115,5066],{},[1919,19117,1921],{},[1148,19119,12587],{"stretchy":1150},[1172,19121,19122],{"encoding":1174},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[1434,19125,19126],{},"right = FALSE"," třídy obrátí na ",[1115,19129,19131],{"className":19130},[1136],[1138,19132,19133],{"xmlns":1140},[1142,19134,19135,19161],{},[1145,19136,19137,19139,19145,19147,19159],{},[1148,19138,13568],{"stretchy":1150},[1217,19140,19141,19143],{},[1156,19142,1262],{},[1156,19144,1934],{},[1148,19146,12041],{"separator":1121},[1217,19148,19149,19151],{},[1156,19150,1262],{},[1145,19152,19153,19155,19157],{},[1156,19154,1934],{},[1148,19156,5066],{},[1919,19158,1921],{},[1148,19160,1170],{"stretchy":1150},[1172,19162,19163],{"encoding":1174},"\\langle c_j; c_{j+1})",[1110,19165,19166],{},[1527,19167],{"alt":19168,"className":19169,"src":19170},"mask-ps-histogram-trideni",[1531,1532],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,19172,19174,19181],{"className":19173,"dataCallout":2145},[1106,2144],[1110,19175,19177,19180],{"className":19176},[1113],[1115,19178],{"className":19179,"ariaHidden":1121},[1118,2152,1120],"Příklad: Třídění datového souboru",[1110,19182,19183],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3261,19185,19187],{"className":3263,"code":19186,"language":71,"meta":3265,"style":3265},"x9 \u003C- c(101, 338, 150, 47, 10, 2, 12, 392, 5, 73,\n        367, 54, 114, 213, 71, 341, 313, 112, 343, 151,\n        9, 160, 18, 113, 77, 71, 159, 12, 119, 130,\n        140, 161, 379, 54, 373, 168, 365, 110, 145, 88,\n        74, 46, 246, 259, 19, 119, 48, 3, 163, 179,\n        194, 33, 49, 501, 193, 19, 5, 2, 221, 300,\n        88, 13, 428, 249, 25, 209, 54, 91)\nlength(x9)\nmax(x9) - min(x9)\ny9 \u003C- hist(x9, br = seq(0, 550, by = 50), right = FALSE, plot = FALSE)\ny9$counts\nround(y9$counts \u002F length(x9), 3)\nmean(x9); sd(x9)\n",[1434,19188,19189,19245,19296,19346,19396,19446,19494,19534,19544,19564,19628,19637,19667],{"__ignoreMap":3265},[1115,19190,19191,19194,19196,19198,19200,19202,19204,19207,19209,19212,19214,19217,19219,19221,19223,19225,19227,19229,19231,19234,19236,19238,19240,19243],{"class":3270,"line":10},[1115,19192,19193],{"class":3280},"x9",[1115,19195,3291],{"class":3273},[1115,19197,4142],{"class":3294},[1115,19199,1151],{"class":3277},[1115,19201,2369],{"class":3312},[1115,19203,1164],{"class":3273},[1115,19205,19206],{"class":3312}," 338",[1115,19208,1164],{"class":3273},[1115,19210,19211],{"class":3312}," 150",[1115,19213,1164],{"class":3273},[1115,19215,19216],{"class":3312}," 47",[1115,19218,1164],{"class":3273},[1115,19220,14616],{"class":3312},[1115,19222,1164],{"class":3273},[1115,19224,4156],{"class":3312},[1115,19226,1164],{"class":3273},[1115,19228,8919],{"class":3312},[1115,19230,1164],{"class":3273},[1115,19232,19233],{"class":3312}," 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88",[1115,19395,8922],{"class":3273},[1115,19397,19398,19401,19403,19406,19408,19411,19413,19416,19418,19421,19423,19425,19427,19430,19432,19434,19436,19439,19441,19444],{"class":3270,"line":96},[1115,19399,19400],{"class":3312},"        74",[1115,19402,1164],{"class":3273},[1115,19404,19405],{"class":3312}," 46",[1115,19407,1164],{"class":3273},[1115,19409,19410],{"class":3312}," 246",[1115,19412,1164],{"class":3273},[1115,19414,19415],{"class":3312}," 259",[1115,19417,1164],{"class":3273},[1115,19419,19420],{"class":3312}," 19",[1115,19422,1164],{"class":3273},[1115,19424,19338],{"class":3312},[1115,19426,1164],{"class":3273},[1115,19428,19429],{"class":3312}," 48",[1115,19431,1164],{"class":3273},[1115,19433,4197],{"class":3312},[1115,19435,1164],{"class":3273},[1115,19437,19438],{"class":3312}," 163",[1115,19440,1164],{"class":3273},[1115,19442,19443],{"class":3312}," 179",[1115,19445,8922],{"class":3273},[1115,19447,19448,19451,19453,19455,19457,19460,19462,19465,19467,19470,19472,19474,19476,19478,19480,19482,19484,19487,19489,19492],{"class":3270,"line":89},[1115,19449,19450],{"class":3312},"        194",[1115,19452,1164],{"class":3273},[1115,19454,9319],{"class":3312},[1115,19456,1164],{"class":3273},[1115,19458,19459],{"class":3312}," 49",[1115,19461,1164],{"class":3273},[1115,19463,19464],{"class":3312}," 501",[1115,19466,1164],{"class":3273},[1115,19468,19469],{"class":3312}," 193",[1115,19471,1164],{"class":3273},[1115,19473,19420],{"class":3312},[1115,19475,1164],{"class":3273},[1115,19477,4161],{"class":3312},[1115,19479,1164],{"class":3273},[1115,19481,4156],{"class":3312},[1115,19483,1164],{"class":3273},[1115,19485,19486],{"class":3312}," 221",[1115,19488,1164],{"class":3273},[1115,19490,19491],{"class":3312}," 300",[1115,19493,8922],{"class":3273},[1115,19495,19496,19499,19501,19503,19505,19508,19510,19513,19515,19518,19520,19523,19525,19527,19529,19532],{"class":3270,"line":82},[1115,19497,19498],{"class":3312},"        88",[1115,19500,1164],{"class":3273},[1115,19502,8914],{"class":3312},[1115,19504,1164],{"class":3273},[1115,19506,19507],{"class":3312}," 428",[1115,19509,1164],{"class":3273},[1115,19511,19512],{"class":3312}," 249",[1115,19514,1164],{"class":3273},[1115,19516,19517],{"class":3312}," 25",[1115,19519,1164],{"class":3273},[1115,19521,19522],{"class":3312}," 209",[1115,19524,1164],{"class":3273},[1115,19526,19254],{"class":3312},[1115,19528,1164],{"class":3273},[1115,19530,19531],{"class":3312}," 91",[1115,19533,3283],{"class":3277},[1115,19535,19536,19538,19540,19542],{"class":3270,"line":75},[1115,19537,17249],{"class":3294},[1115,19539,1151],{"class":3277},[1115,19541,19193],{"class":3280},[1115,19543,3283],{"class":3277},[1115,19545,19546,19548,19550,19552,19554,19556,19558,19560,19562],{"class":3270,"line":9071},[1115,19547,1972],{"class":3294},[1115,19549,1151],{"class":3277},[1115,19551,19193],{"class":3280},[1115,19553,6207],{"class":3277},[1115,19555,6343],{"class":3273},[1115,19557,6231],{"class":3294},[1115,19559,1151],{"class":3277},[1115,19561,19193],{"class":3280},[1115,19563,3283],{"class":3277},[1115,19565,19566,19569,19571,19574,19576,19578,19580,19583,19585,19588,19590,19592,19594,19597,19599,19602,19604,19606,19608,19610,19613,19615,19617,19619,19622,19624,19626],{"class":3270,"line":72},[1115,19567,19568],{"class":3280},"y9",[1115,19570,3291],{"class":3273},[1115,19572,19573],{"class":3294}," hist",[1115,19575,1151],{"class":3277},[1115,19577,19193],{"class":3280},[1115,19579,1164],{"class":3273},[1115,19581,19582],{"class":3280}," br",[1115,19584,3309],{"class":3273},[1115,19586,19587],{"class":3294}," seq",[1115,19589,1151],{"class":3277},[1115,19591,2780],{"class":3312},[1115,19593,1164],{"class":3273},[1115,19595,19596],{"class":3312}," 550",[1115,19598,1164],{"class":3273},[1115,19600,19601],{"class":3280}," by",[1115,19603,3309],{"class":3273},[1115,19605,11402],{"class":3312},[1115,19607,1170],{"class":3277},[1115,19609,1164],{"class":3273},[1115,19611,19612],{"class":3280}," right",[1115,19614,3309],{"class":3273},[1115,19616,11495],{"class":3312},[1115,19618,1164],{"class":3273},[1115,19620,19621],{"class":3280}," plot",[1115,19623,3309],{"class":3273},[1115,19625,11495],{"class":3312},[1115,19627,3283],{"class":3277},[1115,19629,19630,19632,19634],{"class":3270,"line":25},[1115,19631,19568],{"class":3280},[1115,19633,9093],{"class":3273},[1115,19635,19636],{"class":3280},"counts\n",[1115,19638,19639,19641,19643,19645,19647,19650,19652,19655,19657,19659,19661,19663,19665],{"class":3270,"line":65},[1115,19640,15116],{"class":3294},[1115,19642,1151],{"class":3277},[1115,19644,19568],{"class":3280},[1115,19646,9093],{"class":3273},[1115,19648,19649],{"class":3280},"counts",[1115,19651,6292],{"class":3273},[1115,19653,19654],{"class":3294}," length",[1115,19656,1151],{"class":3277},[1115,19658,19193],{"class":3280},[1115,19660,1170],{"class":3277},[1115,19662,1164],{"class":3273},[1115,19664,4197],{"class":3312},[1115,19666,3283],{"class":3277},[1115,19668,19669,19671,19673,19675,19677,19679,19681,19683],{"class":3270,"line":63},[1115,19670,17260],{"class":3294},[1115,19672,1151],{"class":3277},[1115,19674,19193],{"class":3280},[1115,19676,6111],{"class":3277},[1115,19678,17282],{"class":3294},[1115,19680,1151],{"class":3277},[1115,19682,19193],{"class":3280},[1115,19684,3283],{"class":3277},[3261,19686,19689],{"className":19687,"code":19688,"language":4279,"meta":3265},[4277],"[1] 68\n[1] 499\n [1] 19 11 10 10  5  1  5  5  1  0  1\n [1] 0.279 0.162 0.147 0.147 0.074 0.015 0.074 0.074 0.015 0.000 0.015\n[1] 145.4412\n[1] 126.1283\n",[1434,19690,19688],{"__ignoreMap":3265},[1110,19692,19693,19694,19722],{},"Variační rozpětí je ",[1115,19695,19697],{"className":19696},[1136],[1138,19698,19699],{"xmlns":1140},[1142,19700,19701,19719],{},[1145,19702,19703,19705,19707,19710,19712,19714,19716],{},[1156,19704,1167],{},[1148,19706,1914],{},[1919,19708,19709],{},"501",[1148,19711,1990],{},[1919,19713,2302],{},[1148,19715,1914],{},[1919,19717,19718],{},"499",[1172,19720,19721],{"encoding":1174},"R = 501 - 2 = 499"," minut; rozdělit je na 11 tříd po 50 minutách je rozumná volba (ani moc málo, ani moc tříd). Výsledná tabulka četností:",[1459,19724,19725,19821],{},[1462,19726,19727],{},[1465,19728,19729,19744,19763,19782,19801],{},[1468,19730,19731],{},[1115,19732,19734],{"className":19733},[1136],[1138,19735,19736],{"xmlns":1140},[1142,19737,19738,19742],{},[1145,19739,19740],{},[1156,19741,1934],{},[1172,19743,1934],{"encoding":1174},[1468,19745,19746],{},[1115,19747,19749],{"className":19748},[1136],[1138,19750,19751],{"xmlns":1140},[1142,19752,19753,19761],{},[1145,19754,19755],{},[1217,19756,19757,19759],{},[1156,19758,16330],{},[1156,19760,1934],{},[1172,19762,18803],{"encoding":1174},[1468,19764,19765],{},[1115,19766,19768],{"className":19767},[1136],[1138,19769,19770],{"xmlns":1140},[1142,19771,19772,19780],{},[1145,19773,19774],{},[1217,19775,19776,19778],{},[1156,19777,14067],{},[1156,19779,1934],{},[1172,19781,18883],{"encoding":1174},[1468,19783,19784],{},[1115,19785,19787],{"className":19786},[1136],[1138,19788,19789],{"xmlns":1140},[1142,19790,19791,19799],{},[1145,19792,19793],{},[1217,19794,19795,19797],{},[1156,19796,11920],{},[1156,19798,1934],{},[1172,19800,18904],{"encoding":1174},[1468,19802,19803],{},[1115,19804,19806],{"className":19805},[1136],[1138,19807,19808],{"xmlns":1140},[1142,19809,19810,19818],{},[1145,19811,19812],{},[1217,19813,19814,19816],{},[1156,19815,1110],{},[1156,19817,1934],{},[1172,19819,19820],{"encoding":1174},"p_j",[1477,19822,19823,19837,19852,19866,19879,19894,19909,19923,19937,19951,19966],{},[1465,19824,19825,19827,19830,19832,19834],{},[1482,19826,1921],{},[1482,19828,19829],{},"⟨0; 50)",[1482,19831,9232],{},[1482,19833,2464],{},[1482,19835,19836],{},"0,279",[1465,19838,19839,19841,19844,19847,19849],{},[1482,19840,2302],{},[1482,19842,19843],{},"⟨50; 100)",[1482,19845,19846],{},"75",[1482,19848,2644],{},[1482,19850,19851],{},"0,162",[1465,19853,19854,19856,19859,19861,19863],{},[1482,19855,2327],{},[1482,19857,19858],{},"⟨100; 150)",[1482,19860,2474],{},[1482,19862,14175],{},[1482,19864,19865],{},"0,147",[1465,19867,19868,19870,19873,19875,19877],{},[1482,19869,2206],{},[1482,19871,19872],{},"⟨150; 200)",[1482,19874,12623],{},[1482,19876,14175],{},[1482,19878,19865],{},[1465,19880,19881,19883,19886,19889,19891],{},[1482,19882,2424],{},[1482,19884,19885],{},"⟨200; 250)",[1482,19887,19888],{},"225",[1482,19890,2424],{},[1482,19892,19893],{},"0,074",[1465,19895,19896,19898,19901,19904,19906],{},[1482,19897,2437],{},[1482,19899,19900],{},"⟨250; 300)",[1482,19902,19903],{},"275",[1482,19905,1921],{},[1482,19907,19908],{},"0,015",[1465,19910,19911,19913,19916,19919,19921],{},[1482,19912,4147],{},[1482,19914,19915],{},"⟨300; 350)",[1482,19917,19918],{},"325",[1482,19920,2424],{},[1482,19922,19893],{},[1465,19924,19925,19927,19930,19933,19935],{},[1482,19926,2604],{},[1482,19928,19929],{},"⟨350; 400)",[1482,19931,19932],{},"375",[1482,19934,2424],{},[1482,19936,19893],{},[1465,19938,19939,19941,19944,19947,19949],{},[1482,19940,8789],{},[1482,19942,19943],{},"⟨400; 450)",[1482,19945,19946],{},"425",[1482,19948,1921],{},[1482,19950,19908],{},[1465,19952,19953,19955,19958,19961,19963],{},[1482,19954,14175],{},[1482,19956,19957],{},"⟨450; 500)",[1482,19959,19960],{},"475",[1482,19962,2780],{},[1482,19964,19965],{},"0,000",[1465,19967,19968,19970,19973,19976,19978],{},[1482,19969,2644],{},[1482,19971,19972],{},"⟨500; ∞)",[1482,19974,19975],{},"525",[1482,19977,1921],{},[1482,19979,19908],{},[1110,19981,19982,19983,20000,20001,20018,20019,1176,20042,1176,20070,20089,20090,1176,20113,20132],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,19984,19986],{"className":19985},[1136],[1138,19987,19988],{"xmlns":1140},[1142,19989,19990,19998],{},[1145,19991,19992],{},[1217,19993,19994,19996],{},[1156,19995,14067],{},[1156,19997,1934],{},[1172,19999,18883],{"encoding":1174}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,20002,20004],{"className":20003},[1136],[1138,20005,20006],{"xmlns":1140},[1142,20007,20008,20016],{},[1145,20009,20010],{},[1217,20011,20012,20014],{},[1156,20013,14067],{},[1156,20015,1934],{},[1172,20017,18883],{"encoding":1174},") vycházejí ",[1115,20020,20022],{"className":20021},[1136],[1138,20023,20024],{"xmlns":1140},[1142,20025,20026,20039],{},[1145,20027,20028,20034,20036],{},[1153,20029,20030,20032],{"accent":1121},[1156,20031,1158],{},[1148,20033,1161],{},[1148,20035,14579],{},[1919,20037,20038],{},"149,26",[1172,20040,20041],{"encoding":1174},"\\bar{x} \\approx 149{,}26",[1115,20043,20045],{"className":20044},[1136],[1138,20046,20047],{"xmlns":1140},[1142,20048,20049,20067],{},[1145,20050,20051,20057,20059,20062,20064],{},[5465,20052,20053,20055],{},[1156,20054,1198],{},[1919,20056,2302],{},[1148,20058,14579],{},[1919,20060,20061],{},"15",[5009,20063,5011],{},[1919,20065,20066],{},"484,5",[1172,20068,20069],{"encoding":1174},"s^2 \\approx 15\\,484{,}5",[1115,20071,20073],{"className":20072},[1136],[1138,20074,20075],{"xmlns":1140},[1142,20076,20077,20086],{},[1145,20078,20079,20081,20083],{},[1156,20080,1198],{},[1148,20082,14579],{},[1919,20084,20085],{},"124,44",[1172,20087,20088],{"encoding":1174},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,20091,20093],{"className":20092},[1136],[1138,20094,20095],{"xmlns":1140},[1142,20096,20097,20110],{},[1145,20098,20099,20105,20107],{},[1153,20100,20101,20103],{"accent":1121},[1156,20102,1158],{},[1148,20104,1161],{},[1148,20106,1914],{},[1919,20108,20109],{},"145,44",[1172,20111,20112],{"encoding":1174},"\\bar{x}=145{,}44",[1115,20114,20116],{"className":20115},[1136],[1138,20117,20118],{"xmlns":1140},[1142,20119,20120,20129],{},[1145,20121,20122,20124,20126],{},[1156,20123,1198],{},[1148,20125,1914],{},[1919,20127,20128],{},"126,13",[1172,20130,20131],{"encoding":1174},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,20134,20135,20136,20139,20140,20176,20177,20195,20196,20210,20211,20237,20238,20240,20241,10026],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1445,20137,20138],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,20141,20143],{"className":20142},[1136],[1138,20144,20145],{"xmlns":1140},[1142,20146,20147,20173],{},[1145,20148,20149,20151,20153,20155,20157,20159,20161],{},[1156,20150,11920],{},[1148,20152,1151],{"stretchy":1150},[1156,20154,1158],{},[1148,20156,1170],{"stretchy":1150},[1148,20158,1914],{},[1156,20160,14850],{},[5465,20162,20163,20165],{},[1156,20164,13735],{},[1145,20166,20167,20169,20171],{},[1148,20168,1990],{},[1156,20170,14850],{},[1156,20172,1158],{},[1172,20174,20175],{"encoding":1174},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,20178,20180],{"className":20179},[1136],[1138,20181,20182],{"xmlns":1140},[1142,20183,20184,20192],{},[1145,20185,20186,20188,20190],{},[1156,20187,1158],{},[1148,20189,8553],{},[1919,20191,2780],{},[1172,20193,20194],{"encoding":1174},"x \\ge 0",", s parametrem ",[1115,20197,20199],{"className":20198},[1136],[1138,20200,20201],{"xmlns":1140},[1142,20202,20203,20207],{},[1145,20204,20205],{},[1156,20206,14850],{},[1172,20208,20209],{"encoding":1174},"\\lambda"," odhadnutým jako ",[1115,20212,20214],{"className":20213},[1136],[1138,20215,20216],{"xmlns":1140},[1142,20217,20218,20234],{},[1145,20219,20220,20222,20224,20226,20228],{},[1156,20221,14850],{},[1148,20223,1914],{},[1919,20225,1921],{},[1156,20227,4412],{"mathvariant":2014},[1153,20229,20230,20232],{"accent":1121},[1156,20231,1158],{},[1148,20233,1161],{},[1172,20235,20236],{"encoding":1174},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[1434,20239,15017],{}," parametrem ",[1434,20242,20243],{},"dexp()",[3261,20245,20247],{"className":3263,"code":20246,"language":71,"meta":3265,"style":3265},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[1434,20248,20249,20268],{"__ignoreMap":3265},[1115,20250,20251,20254,20256,20258,20260,20262,20264,20266],{"class":3270,"line":10},[1115,20252,20253],{"class":3280},"rate9",[1115,20255,3291],{"class":3273},[1115,20257,3882],{"class":3312},[1115,20259,6292],{"class":3273},[1115,20261,6104],{"class":3294},[1115,20263,1151],{"class":3277},[1115,20265,19193],{"class":3280},[1115,20267,3283],{"class":3277},[1115,20269,20270],{"class":3270,"line":27},[1115,20271,20272],{"class":3280},"rate9\n",[3261,20274,20277],{"className":20275,"code":20276,"language":4279,"meta":3265},[4277],"[1] 0.006875632\n",[1434,20278,20276],{"__ignoreMap":3265},[1110,20280,20281],{},[1527,20282],{"alt":20283,"className":20284,"src":20285},"mask-ps-hustota-fit",[1531,1532],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,20287,20288,20289,1247],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[6613,20290,11762],{"className":20291,"dataFsResolvedFilePath":6639,"href":6640},[1531],[1103,20293,20295,20302],{"className":20294,"dataCallout":2145},[1106,2144],[1110,20296,20298,20301],{"className":20297},[1113],[1115,20299],{"className":20300,"ariaHidden":1121},[1118,2152,1120],"Příklad: Doba života výrobku",[1110,20303,20304],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3261,20306,20308],{"className":3263,"code":20307,"language":71,"meta":3265,"style":3265},"x5 \u003C- c(63, 156, 184, 786, 822, 278, 15, 561, 229, 8,\n        4, 35, 73, 203, 178, 323, 275, 176, 427, 196,\n        415, 140, 17, 293, 991, 100, 189, 176, 672, 134,\n        529, 310, 22, 69, 130, 272, 117, 169, 466, 286,\n        46, 236, 387, 92, 177, 188, 124, 385, 174, 23)\nlength(x5)\nmean(x5); sd(x5); median(x5)\nmax(x5) - min(x5)\ny5 \u003C- hist(x5, br = seq(0, 1050, by = 150), right = FALSE, plot = FALSE)\ny5$mids\ny5$counts\nround(y5$counts \u002F length(x5), 3)\n",[1434,20309,20310,20371,20422,20472,20523,20575,20585,20611,20631,20689,20698,20706],{"__ignoreMap":3265},[1115,20311,20312,20315,20317,20319,20321,20324,20326,20329,20331,20334,20336,20339,20341,20344,20346,20349,20351,20354,20356,20359,20361,20364,20366,20369],{"class":3270,"line":10},[1115,20313,20314],{"class":3280},"x5",[1115,20316,3291],{"class":3273},[1115,20318,4142],{"class":3294},[1115,20320,1151],{"class":3277},[1115,20322,20323],{"class":3312},"63",[1115,20325,1164],{"class":3273},[1115,20327,20328],{"class":3312}," 156",[1115,20330,1164],{"class":3273},[1115,20332,20333],{"class":3312}," 184",[1115,20335,1164],{"class":3273},[1115,20337,20338],{"class":3312}," 786",[1115,20340,1164],{"class":3273},[1115,20342,20343],{"class":3312}," 822",[1115,20345,1164],{"class":3273},[1115,20347,20348],{"class":3312}," 278",[1115,20350,1164],{"class":3273},[1115,20352,20353],{"class":3312}," 15",[1115,20355,1164],{"class":3273},[1115,20357,20358],{"class":3312}," 561",[1115,20360,1164],{"class":3273},[1115,20362,20363],{"class":3312}," 229",[1115,20365,1164],{"class":3273},[1115,20367,20368],{"class":3312}," 8",[1115,20370,8922],{"class":3273},[1115,20372,20373,20376,20378,20381,20383,20385,20387,20390,20392,20395,20397,20400,20402,20405,20407,20410,20412,20415,20417,20420],{"class":3270,"line":27},[1115,20374,20375],{"class":3312},"        4",[1115,20377,1164],{"class":3273},[1115,20379,20380],{"class":3312}," 35",[1115,20382,1164],{"class":3273},[1115,20384,19242],{"class":3312},[1115,20386,1164],{"class":3273},[1115,20388,20389],{"class":3312}," 203",[1115,20391,1164],{"class":3273},[1115,20393,20394],{"class":3312}," 178",[1115,20396,1164],{"class":3273},[1115,20398,20399],{"class":3312}," 323",[1115,20401,1164],{"class":3273},[1115,20403,20404],{"class":3312}," 275",[1115,20406,1164],{"class":3273},[1115,20408,20409],{"class":3312}," 176",[1115,20411,1164],{"class":3273},[1115,20413,20414],{"class":3312}," 427",[1115,20416,1164],{"class":3273},[1115,20418,20419],{"class":3312}," 196",[1115,20421,8922],{"class":3273},[1115,20423,20424,20427,20429,20432,20434,20437,20439,20442,20444,20447,20449,20451,20453,20456,20458,20460,20462,20465,20467,20470],{"class":3270,"line":148},[1115,20425,20426],{"class":3312},"        415",[1115,20428,1164],{"class":3273},[1115,20430,20431],{"class":3312}," 140",[1115,20433,1164],{"class":3273},[1115,20435,20436],{"class":3312}," 17",[1115,20438,1164],{"class":3273},[1115,20440,20441],{"class":3312}," 293",[1115,20443,1164],{"class":3273},[1115,20445,20446],{"class":3312}," 991",[1115,20448,1164],{"class":3273},[1115,20450,4655],{"class":3312},[1115,20452,1164],{"class":3273},[1115,20454,20455],{"class":3312}," 189",[1115,20457,1164],{"class":3273},[1115,20459,20409],{"class":3312},[1115,20461,1164],{"class":3273},[1115,20463,20464],{"class":3312}," 672",[1115,20466,1164],{"class":3273},[1115,20468,20469],{"class":3312}," 134",[1115,20471,8922],{"class":3273},[1115,20473,20474,20477,20479,20482,20484,20487,20489,20492,20494,20496,20498,20501,20503,20506,20508,20511,20513,20516,20518,20521],{"class":3270,"line":111},[1115,20475,20476],{"class":3312},"        529",[1115,20478,1164],{"class":3273},[1115,20480,20481],{"class":3312}," 310",[1115,20483,1164],{"class":3273},[1115,20485,20486],{"class":3312}," 22",[1115,20488,1164],{"class":3273},[1115,20490,20491],{"class":3312}," 69",[1115,20493,1164],{"class":3273},[1115,20495,19343],{"class":3312},[1115,20497,1164],{"class":3273},[1115,20499,20500],{"class":3312}," 272",[1115,20502,1164],{"class":3273},[1115,20504,20505],{"class":3312}," 117",[1115,20507,1164],{"class":3273},[1115,20509,20510],{"class":3312}," 169",[1115,20512,1164],{"class":3273},[1115,20514,20515],{"class":3312}," 466",[1115,20517,1164],{"class":3273},[1115,20519,20520],{"class":3312}," 286",[1115,20522,8922],{"class":3273},[1115,20524,20525,20528,20530,20533,20535,20538,20540,20543,20545,20548,20550,20553,20555,20558,20560,20563,20565,20568,20570,20573],{"class":3270,"line":96},[1115,20526,20527],{"class":3312},"        46",[1115,20529,1164],{"class":3273},[1115,20531,20532],{"class":3312}," 236",[1115,20534,1164],{"class":3273},[1115,20536,20537],{"class":3312}," 387",[1115,20539,1164],{"class":3273},[1115,20541,20542],{"class":3312}," 92",[1115,20544,1164],{"class":3273},[1115,20546,20547],{"class":3312}," 177",[1115,20549,1164],{"class":3273},[1115,20551,20552],{"class":3312}," 188",[1115,20554,1164],{"class":3273},[1115,20556,20557],{"class":3312}," 124",[1115,20559,1164],{"class":3273},[1115,20561,20562],{"class":3312}," 385",[1115,20564,1164],{"class":3273},[1115,20566,20567],{"class":3312}," 174",[1115,20569,1164],{"class":3273},[1115,20571,20572],{"class":3312}," 23",[1115,20574,3283],{"class":3277},[1115,20576,20577,20579,20581,20583],{"class":3270,"line":89},[1115,20578,17249],{"class":3294},[1115,20580,1151],{"class":3277},[1115,20582,20314],{"class":3280},[1115,20584,3283],{"class":3277},[1115,20586,20587,20589,20591,20593,20595,20597,20599,20601,20603,20605,20607,20609],{"class":3270,"line":82},[1115,20588,17260],{"class":3294},[1115,20590,1151],{"class":3277},[1115,20592,20314],{"class":3280},[1115,20594,6111],{"class":3277},[1115,20596,17282],{"class":3294},[1115,20598,1151],{"class":3277},[1115,20600,20314],{"class":3280},[1115,20602,6111],{"class":3277},[1115,20604,17978],{"class":3294},[1115,20606,1151],{"class":3277},[1115,20608,20314],{"class":3280},[1115,20610,3283],{"class":3277},[1115,20612,20613,20615,20617,20619,20621,20623,20625,20627,20629],{"class":3270,"line":75},[1115,20614,1972],{"class":3294},[1115,20616,1151],{"class":3277},[1115,20618,20314],{"class":3280},[1115,20620,6207],{"class":3277},[1115,20622,6343],{"class":3273},[1115,20624,6231],{"class":3294},[1115,20626,1151],{"class":3277},[1115,20628,20314],{"class":3280},[1115,20630,3283],{"class":3277},[1115,20632,20633,20636,20638,20640,20642,20644,20646,20648,20650,20652,20654,20656,20658,20661,20663,20665,20667,20669,20671,20673,20675,20677,20679,20681,20683,20685,20687],{"class":3270,"line":9071},[1115,20634,20635],{"class":3280},"y5",[1115,20637,3291],{"class":3273},[1115,20639,19573],{"class":3294},[1115,20641,1151],{"class":3277},[1115,20643,20314],{"class":3280},[1115,20645,1164],{"class":3273},[1115,20647,19582],{"class":3280},[1115,20649,3309],{"class":3273},[1115,20651,19587],{"class":3294},[1115,20653,1151],{"class":3277},[1115,20655,2780],{"class":3312},[1115,20657,1164],{"class":3273},[1115,20659,20660],{"class":3312}," 1050",[1115,20662,1164],{"class":3273},[1115,20664,19601],{"class":3280},[1115,20666,3309],{"class":3273},[1115,20668,19211],{"class":3312},[1115,20670,1170],{"class":3277},[1115,20672,1164],{"class":3273},[1115,20674,19612],{"class":3280},[1115,20676,3309],{"class":3273},[1115,20678,11495],{"class":3312},[1115,20680,1164],{"class":3273},[1115,20682,19621],{"class":3280},[1115,20684,3309],{"class":3273},[1115,20686,11495],{"class":3312},[1115,20688,3283],{"class":3277},[1115,20690,20691,20693,20695],{"class":3270,"line":72},[1115,20692,20635],{"class":3280},[1115,20694,9093],{"class":3273},[1115,20696,20697],{"class":3280},"mids\n",[1115,20699,20700,20702,20704],{"class":3270,"line":25},[1115,20701,20635],{"class":3280},[1115,20703,9093],{"class":3273},[1115,20705,19636],{"class":3280},[1115,20707,20708,20710,20712,20714,20716,20718,20720,20722,20724,20726,20728,20730,20732],{"class":3270,"line":65},[1115,20709,15116],{"class":3294},[1115,20711,1151],{"class":3277},[1115,20713,20635],{"class":3280},[1115,20715,9093],{"class":3273},[1115,20717,19649],{"class":3280},[1115,20719,6292],{"class":3273},[1115,20721,19654],{"class":3294},[1115,20723,1151],{"class":3277},[1115,20725,20314],{"class":3280},[1115,20727,1170],{"class":3277},[1115,20729,1164],{"class":3273},[1115,20731,4197],{"class":3312},[1115,20733,3283],{"class":3277},[3261,20735,20738],{"className":20736,"code":20737,"language":4279,"meta":3265},[4277],"[1] 50\n[1] 246.42\n[1] 220.0209\n[1] 181\n[1] 987\n[1]   75 225 375 525 675 825 975\n[1] 18 19  6  3  1  2  1\n[1] 0.36 0.38 0.12 0.06 0.02 0.04 0.02\n",[1434,20739,20737],{"__ignoreMap":3265},[1110,20741,20742],{},"Variační rozpětí 987 minut rozdělené do 7 tříd po 150 minutách dává podobný tvar jako u předchozího příkladu: 74 % výrobků vydrželo méně než 300 minut, ojedinělé hodnoty sahají až k 991 minutám. Průměr 246,4 minuty leží výrazně nad mediánem 181 minut — rozdělení je zešikmené k vyšším hodnotám stejně jako u doby do poruchy výše.",[1437,20744,6378],{"id":6377},[1124,20746,20747,20765,20866,20934],{},[1127,20748,20749,6884,20752,20755,20756,20759,20760,20762,20763,1247],{},[1445,20750,20751],{},"Výchozí typ kvantilu v R.",[1434,20753,20754],{},"quantile()"," bez argumentu ",[1434,20757,20758],{},"type"," používá jiný výpočetní vzorec (",[1434,20761,17409],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[1434,20764,17405],{},[1127,20766,20767,20772,20773,20775,20776,20811,20812,20847,20848,20865],{},[1445,20768,20769,20770,1247],{},"Výchozí ohraničení tříd v ",[1434,20771,19000],{}," Bez ",[1434,20774,19126],{}," jsou třídy zprava uzavřené, ",[1115,20777,20779],{"className":20778},[1136],[1138,20780,20781],{"xmlns":1140},[1142,20782,20783,20809],{},[1145,20784,20785,20787,20793,20795,20807],{},[1148,20786,1151],{"stretchy":1150},[1217,20788,20789,20791],{},[1156,20790,1262],{},[1156,20792,1934],{},[1148,20794,12041],{"separator":1121},[1217,20796,20797,20799],{},[1156,20798,1262],{},[1145,20800,20801,20803,20805],{},[1156,20802,1934],{},[1148,20804,5066],{},[1919,20806,1921],{},[1148,20808,12587],{"stretchy":1150},[1172,20810,19122],{"encoding":1174}," — opačně než konvence ",[1115,20813,20815],{"className":20814},[1136],[1138,20816,20817],{"xmlns":1140},[1142,20818,20819,20845],{},[1145,20820,20821,20823,20829,20831,20843],{},[1148,20822,13568],{"stretchy":1150},[1217,20824,20825,20827],{},[1156,20826,1262],{},[1156,20828,1934],{},[1148,20830,12041],{"separator":1121},[1217,20832,20833,20835],{},[1156,20834,1262],{},[1145,20836,20837,20839,20841],{},[1156,20838,1934],{},[1148,20840,5066],{},[1919,20842,1921],{},[1148,20844,1170],{"stretchy":1150},[1172,20846,19163],{"encoding":1174}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,20849,20851],{"className":20850},[1136],[1138,20852,20853],{"xmlns":1140},[1142,20854,20855,20863],{},[1145,20856,20857],{},[1217,20858,20859,20861],{},[1156,20860,11920],{},[1156,20862,1934],{},[1172,20864,18904],{"encoding":1174}," vyjdou jinak.",[1127,20867,20868,6884,20871,20889,20890,20903,20904,14190,20917,1247],{},[1445,20869,20870],{},"Rozptyl vs. směrodatná odchylka.",[1115,20872,20874],{"className":20873},[1136],[1138,20875,20876],{"xmlns":1140},[1142,20877,20878,20886],{},[1145,20879,20880],{},[5465,20881,20882,20884],{},[1156,20883,1198],{},[1919,20885,2302],{},[1172,20887,20888],{"encoding":1174},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,20891,20893],{"className":20892},[1136],[1138,20894,20895],{"xmlns":1140},[1142,20896,20897,20901],{},[1145,20898,20899],{},[1156,20900,1198],{},[1172,20902,1198],{"encoding":1174}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,20905,20907],{"className":20906},[1136],[1138,20908,20909],{"xmlns":1140},[1142,20910,20911,20915],{},[1145,20912,20913],{},[1156,20914,1198],{},[1172,20916,1198],{"encoding":1174},[1115,20918,20920],{"className":20919},[1136],[1138,20921,20922],{"xmlns":1140},[1142,20923,20924,20932],{},[1145,20925,20926],{},[5465,20927,20928,20930],{},[1156,20929,1198],{},[1919,20931,2302],{},[1172,20933,20888],{"encoding":1174},[1127,20935,20936,20939],{},[1445,20937,20938],{},"Příliš mnoho nebo příliš málo tříd."," Málo tříd skryje tvar rozdělení, moc tříd rozmělní četnosti na jednotky a histogram je nečitelný; volí se kompromis, ne pevné pravidlo.",[1437,20941,6607],{"id":6606},[1124,20943,20944,20949,20954,20959,20964,20969,20974],{},[1127,20945,20946],{},[6613,20947,6618],{"className":20948,"dataFsResolvedFilePath":6616,"href":6617},[1531],[1127,20950,20951],{},[6613,20952,11774],{"className":20953,"dataFsResolvedFilePath":6631,"href":6632},[1531],[1127,20955,20956],{},[6613,20957,11762],{"className":20958,"dataFsResolvedFilePath":6639,"href":6640},[1531],[1127,20960,20961],{},[6613,20962,11780],{"className":20963,"dataFsResolvedFilePath":6646,"href":6647},[1531],[1127,20965,20966],{},[6613,20967,6754],{"className":20968,"dataFsResolvedFilePath":6654,"href":6655},[1531],[1127,20970,20971],{},[6613,20972,1094],{"className":20973,"dataFsResolvedFilePath":11786,"href":11787},[1531],[1127,20975,20976],{},[6613,20977,6663],{"className":20978,"dataFsResolvedFilePath":6661,"href":6662},[1531],[1437,20980,6666],{"id":934},[1110,20982,6669,20983,6674],{},[6671,20984,6673],{},[6697,20986,20987],{},"html pre.shiki code .sP4rz, 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analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,21035,21037],{"className":21036},[1136],[1138,21038,21039],{"xmlns":1140},[1142,21040,21041,21045],{},[1145,21042,21043],{},[1156,21044,12274],{},[1172,21046,12274],{"encoding":1174}," na vysvětlujících proměnných ",[1115,21049,21051],{"className":21050},[1136],[1138,21052,21053],{"xmlns":1140},[1142,21054,21055,21059],{},[1145,21056,21057],{},[1156,21058,1158],{},[1172,21060,1158],{"encoding":1174}," (příčina → následek); ",[1445,21063,21064],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1127,21067,21068,21069,21072,21073,1247],{},"Parametry regresní funkce se odhadují ",[1445,21070,21071],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,21074,21076],{"className":21075},[1136],[1138,21077,21078],{"xmlns":1140},[1142,21079,21080,21110],{},[1145,21081,21082,21084,21086,21092,21094,21104],{},[1148,21083,1929],{},[1148,21085,1151],{"stretchy":1150},[1217,21087,21088,21090],{},[1156,21089,12274],{},[1156,21091,1223],{},[1148,21093,1990],{},[1217,21095,21096,21102],{},[1153,21097,21098,21100],{"accent":1121},[1156,21099,12274],{},[1148,21101,6165],{},[1156,21103,1223],{},[5465,21105,21106,21108],{},[1148,21107,1170],{"stretchy":1150},[1919,21109,2302],{},[1172,21111,21112],{"encoding":1174},"\\sum(y_i-\\hat y_i)^2",[1127,21114,21115,21116,6884,21119,21137,21138,6884,21141,21165,21166,6884,21169,1247],{},"Kvalitu fitu měří ",[1445,21117,21118],{},"index determinace",[1115,21120,21122],{"className":21121},[1136],[1138,21123,21124],{"xmlns":1140},[1142,21125,21126,21134],{},[1145,21127,21128],{},[5465,21129,21130,21132],{},[1156,21131,1167],{},[1919,21133,2302],{},[1172,21135,21136],{"encoding":1174},"R^2","; obecnou těsnost závislosti ",[1445,21139,21140],{},"index korelace",[1115,21142,21144],{"className":21143},[1136],[1138,21145,21146],{"xmlns":1140},[1142,21147,21148,21162],{},[1145,21149,21150,21152,21154],{},[1156,21151,16330],{},[1148,21153,1914],{},[5460,21155,21156],{},[5465,21157,21158,21160],{},[1156,21159,1167],{},[1919,21161,2302],{},[1172,21163,21164],{"encoding":1174},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1445,21167,21168],{},"koeficientu korelace",[1115,21170,21172],{"className":21171},[1136],[1138,21173,21174],{"xmlns":1140},[1142,21175,21176,21188],{},[1145,21177,21178],{},[1217,21179,21180,21182],{},[1156,21181,71],{},[1145,21183,21184,21186],{},[1156,21185,1158],{},[1156,21187,12274],{},[1172,21189,21190],{"encoding":1174},"r_{xy}",[1127,21192,21193,21194,21197,21198,21201,21202,21205],{},"Když přímka nestačí, volí se ",[1445,21195,21196],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1445,21199,21200],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[1434,21203,21204],{},"nls2",").",[1127,21207,21208,21211],{},[1445,21209,21210],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1127,21213,21214,21215,1176,21218,1176,21221,1176,21224,1176,21227,1176,21230,1176,21233,1176,21236,1176,21239,1176,21242,1247],{},"V R: ",[1434,21216,21217],{},"lm()",[1434,21219,21220],{},"nls2()",[1434,21222,21223],{},"summary()",[1434,21225,21226],{},"confint()",[1434,21228,21229],{},"predict()",[1434,21231,21232],{},"step()",[1434,21234,21235],{},"car::vif()",[1434,21237,21238],{},"lmtest::dwtest()",[1434,21240,21241],{},"whitestrap::white_test()",[1434,21243,21244],{},"shapiro.test()",[1437,21246,16367],{"id":16366},[1110,21248,21249,21252,21253,1204,21266,21279,21280,21282,21283,21296,21297,21310,21311,21314],{},[6613,21250,6618],{"className":21251,"dataFsResolvedFilePath":6616,"href":6617},[1531]," pracuje se dvěma znaky ",[1115,21254,21256],{"className":21255},[1136],[1138,21257,21258],{"xmlns":1140},[1142,21259,21260,21264],{},[1145,21261,21262],{},[1156,21263,1158],{},[1172,21265,1158],{"encoding":1174},[1115,21267,21269],{"className":21268},[1136],[1138,21270,21271],{"xmlns":1140},[1142,21272,21273,21277],{},[1145,21274,21275],{},[1156,21276,12274],{},[1172,21278,12274],{"encoding":1174}," zjištěnými na stejných jednotkách. ",[1445,21281,21032],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,21284,21286],{"className":21285},[1136],[1138,21287,21288],{"xmlns":1140},[1142,21289,21290,21294],{},[1145,21291,21292],{},[1156,21293,1158],{},[1172,21295,1158],{"encoding":1174}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,21298,21300],{"className":21299},[1136],[1138,21301,21302],{"xmlns":1140},[1142,21303,21304,21308],{},[1145,21305,21306],{},[1156,21307,12274],{},[1172,21309,12274],{"encoding":1174}," v úloze následku. ",[1445,21312,21313],{},"Korelační analýza"," se zabývá vzájemnými, většinou lineárními závislostmi; důraz je kladen na intenzitu vztahu. Oba přístupy se v praxi prolínají — nejdřív se zvolí a odhadne regresní funkce, pak se její kvalita vyjádří korelační charakteristikou.",[1110,21316,21317,21318,21205],{},"Hlavním úkolem obou analýz je přispět k poznání vztahů mezi znaky — podat matematický popis systematických okolností, které závislost provázejí, a nalézt funkci, která nejlépe vystihuje její charakter (",[1445,21319,21320],{},"regresní funkce",[1110,21322,21323],{},"Druh regresní analýzy určuje struktura datového souboru:",[1124,21325,21326,21363],{},[1127,21327,21328,21331,21332,21345,21346,21359,21360,1164],{},[1445,21329,21330],{},"dvourozměrný datový soubor"," (jedna ",[1115,21333,21335],{"className":21334},[1136],[1138,21336,21337],{"xmlns":1140},[1142,21338,21339,21343],{},[1145,21340,21341],{},[1156,21342,1158],{},[1172,21344,1158],{"encoding":1174},", jedna ",[1115,21347,21349],{"className":21348},[1136],[1138,21350,21351],{"xmlns":1140},[1142,21352,21353,21357],{},[1145,21354,21355],{},[1156,21356,12274],{},[1172,21358,12274],{"encoding":1174},") → ",[1445,21361,21362],{},"regresní analýza dvou proměnných",[1127,21364,21365,21368,21369,21359,21399,1247],{},[1445,21366,21367],{},"vícerozměrný datový soubor"," (více ",[1115,21370,21372],{"className":21371},[1136],[1138,21373,21374],{"xmlns":1140},[1142,21375,21376,21396],{},[1145,21377,21378,21384,21386,21388,21390],{},[1217,21379,21380,21382],{},[1156,21381,1158],{},[1919,21383,1921],{},[1148,21385,1164],{"separator":1121},[1148,21387,2043],{},[1148,21389,1164],{"separator":1121},[1217,21391,21392,21394],{},[1156,21393,1158],{},[1156,21395,1110],{},[1172,21397,21398],{"encoding":1174},"x_1,\\dots,x_p",[1445,21400,21401],{},"vícenásobná regresní analýza",[1110,21403,21404,21405,21408,21409,21412],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1445,21406,21407],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1445,21410,21411],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1437,21414,21416],{"id":21415},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,21418,21419,21420,6884,21423,21477,21478,21496,21497,6884,21500,21556,21557,21575,21576,21593,21594,21632,21633,1247],{},"Rozlišují se ",[1445,21421,21422],{},"teoretická regresní funkce",[1115,21424,21426],{"className":21425},[1136],[1138,21427,21428],{"xmlns":1140},[1142,21429,21430,21474],{},[1145,21431,21432,21435,21437,21439,21441,21443,21445,21452,21454,21460,21462,21464,21466,21472],{},[1156,21433,21434],{},"η",[1148,21436,1914],{},[1156,21438,11920],{},[1148,21440,1151],{"stretchy":1150},[1156,21442,1158],{},[1148,21444,12041],{"separator":1121},[1217,21446,21447,21450],{},[1156,21448,21449],{},"β",[1919,21451,2780],{},[1148,21453,1164],{"separator":1121},[1217,21455,21456,21458],{},[1156,21457,21449],{},[1919,21459,1921],{},[1148,21461,1164],{"separator":1121},[1148,21463,2043],{},[1148,21465,1164],{"separator":1121},[1217,21467,21468,21470],{},[1156,21469,21449],{},[1156,21471,1110],{},[1148,21473,1170],{"stretchy":1150},[1172,21475,21476],{"encoding":1174},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,21479,21481],{"className":21480},[1136],[1138,21482,21483],{"xmlns":1140},[1142,21484,21485,21493],{},[1145,21486,21487],{},[1217,21488,21489,21491],{},[1156,21490,21449],{},[1156,21492,1223],{},[1172,21494,21495],{"encoding":1174},"\\beta_i"," — a ",[1445,21498,21499],{},"empirická regresní funkce",[1115,21501,21503],{"className":21502},[1136],[1138,21504,21505],{"xmlns":1140},[1142,21506,21507,21553],{},[1145,21508,21509,21515,21517,21519,21521,21523,21525,21531,21533,21539,21541,21543,21545,21551],{},[1153,21510,21511,21513],{"accent":1121},[1156,21512,12274],{},[1148,21514,6165],{},[1148,21516,1914],{},[1156,21518,11920],{},[1148,21520,1151],{"stretchy":1150},[1156,21522,1158],{},[1148,21524,12041],{"separator":1121},[1217,21526,21527,21529],{},[1156,21528,16632],{},[1919,21530,2780],{},[1148,21532,1164],{"separator":1121},[1217,21534,21535,21537],{},[1156,21536,16632],{},[1919,21538,1921],{},[1148,21540,1164],{"separator":1121},[1148,21542,2043],{},[1148,21544,1164],{"separator":1121},[1217,21546,21547,21549],{},[1156,21548,16632],{},[1156,21550,1110],{},[1148,21552,1170],{"stretchy":1150},[1172,21554,21555],{"encoding":1174},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,21558,21560],{"className":21559},[1136],[1138,21561,21562],{"xmlns":1140},[1142,21563,21564,21572],{},[1145,21565,21566],{},[1217,21567,21568,21570],{},[1156,21569,16632],{},[1156,21571,1223],{},[1172,21573,21574],{"encoding":1174},"b_i"," jsou odhadem ",[1115,21577,21579],{"className":21578},[1136],[1138,21580,21581],{"xmlns":1140},[1142,21582,21583,21591],{},[1145,21584,21585],{},[1217,21586,21587,21589],{},[1156,21588,21449],{},[1156,21590,1223],{},[1172,21592,21495],{"encoding":1174}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,21595,21597],{"className":21596},[1136],[1138,21598,21599],{"xmlns":1140},[1142,21600,21601,21629],{},[1145,21602,21603,21609,21611,21617,21619],{},[1217,21604,21605,21607],{},[1156,21606,13735],{},[1156,21608,1223],{},[1148,21610,1914],{},[1217,21612,21613,21615],{},[1156,21614,12274],{},[1156,21616,1223],{},[1148,21618,1990],{},[1217,21620,21621,21627],{},[1153,21622,21623,21625],{"accent":1121},[1156,21624,12274],{},[1148,21626,6165],{},[1156,21628,1223],{},[1172,21630,21631],{"encoding":1174},"e_i=y_i-\\hat y_i",", se nazývají ",[1445,21634,21635],{},"rezidua",[1110,21637,21638,21639,21642],{},"Nejpoužívanější metodou odhadu parametrů je ",[1445,21640,21641],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,21644,21646],{"className":21645},[1136],[1138,21647,21648],{"xmlns":1140,"display":1897},[1142,21649,21650,21700],{},[1145,21651,21652,21666,21668,21674,21676,21686,21692,21694,21696,21698],{},[1925,21653,21654,21656,21664],{},[1148,21655,1929],{},[1145,21657,21658,21660,21662],{},[1156,21659,1223],{},[1148,21661,1914],{},[1919,21663,1921],{},[1156,21665,1292],{},[1148,21667,1151],{"stretchy":1150},[1217,21669,21670,21672],{},[1156,21671,12274],{},[1156,21673,1223],{},[1148,21675,1990],{},[1217,21677,21678,21684],{},[1153,21679,21680,21682],{"accent":1121},[1156,21681,12274],{},[1148,21683,6165],{},[1156,21685,1223],{},[5465,21687,21688,21690],{},[1148,21689,1170],{"stretchy":1150},[1919,21691,2302],{},[1148,21693,12751],{},[1156,21695,1997],{},[1148,21697,1975],{},[1156,21699,1247],{"mathvariant":2014},[1172,21701,21702],{"encoding":1174},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,21704,21705],{},"Odhad probíhá ve čtyřech krocích: (1) posoudit dostupné informace o charakteru závislosti, (2) navrhnout jeden nebo víc typů regresních funkcí, (3) odhadnout jejich parametry metodou nejmenších čtverců, (4) porovnat vhodnost odhadnutých funkcí a při neuspokojivém výsledku zvolit jiný typ.",[1110,21707,21708],{},[1527,21709],{"alt":21710,"className":21711,"src":21712},"mask-ra-primka-rezidua",[1531,1532],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,21714,21715,21716,21734],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,21717,21719],{"className":21718},[1136],[1138,21720,21721],{"xmlns":1140},[1142,21722,21723,21731],{},[1145,21724,21725],{},[1217,21726,21727,21729],{},[1156,21728,13735],{},[1156,21730,1223],{},[1172,21732,21733],{"encoding":1174},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1437,21736,21738],{"id":21737},"regresní-přímka","Regresní přímka",[1110,21740,21741,21742,2529],{},"Nejjednodušší regresní funkcí je ",[1445,21743,21744],{},"regresní přímka",[1115,21746,21748],{"className":21747},[1136],[1138,21749,21750],{"xmlns":1140,"display":1897},[1142,21751,21752,21804],{},[1145,21753,21754,21756,21758,21764,21766,21772,21774,21776,21778,21784,21786,21792,21794,21800,21802],{},[1156,21755,21434],{},[1148,21757,1914],{},[1217,21759,21760,21762],{},[1156,21761,21449],{},[1919,21763,2780],{},[1148,21765,5066],{},[1217,21767,21768,21770],{},[1156,21769,21449],{},[1919,21771,1921],{},[1156,21773,1158],{},[1148,21775,1164],{"separator":1121},[1954,21777],{"width":1956},[1153,21779,21780,21782],{"accent":1121},[1156,21781,12274],{},[1148,21783,6165],{},[1148,21785,1914],{},[1217,21787,21788,21790],{},[1156,21789,16632],{},[1919,21791,2780],{},[1148,21793,5066],{},[1217,21795,21796,21798],{},[1156,21797,16632],{},[1919,21799,1921],{},[1156,21801,1158],{},[1156,21803,1247],{"mathvariant":2014},[1172,21805,21806],{"encoding":1174},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,21808,21809,21810,21828,21829,21842,21843,21856],{},"Koeficient ",[1115,21811,21813],{"className":21812},[1136],[1138,21814,21815],{"xmlns":1140},[1142,21816,21817,21825],{},[1145,21818,21819],{},[1217,21820,21821,21823],{},[1156,21822,16632],{},[1919,21824,1921],{},[1172,21826,21827],{"encoding":1174},"b_1"," udává změnu průměru ",[1115,21830,21832],{"className":21831},[1136],[1138,21833,21834],{"xmlns":1140},[1142,21835,21836,21840],{},[1145,21837,21838],{},[1156,21839,12274],{},[1172,21841,12274],{"encoding":1174}," při jednotkové změně ",[1115,21844,21846],{"className":21845},[1136],[1138,21847,21848],{"xmlns":1140},[1142,21849,21850,21854],{},[1145,21851,21852],{},[1156,21853,1158],{},[1172,21855,1158],{"encoding":1174},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[1818,21858,21860],{"id":21859},"v-r","V R",[1110,21862,21863,21864,21867,21868,21871],{},"Vstupní data se nahrají buď ze souboru (",[1434,21865,21866],{},"d \u003C- read.table(\"data.txt\")",", případně ",[1434,21869,21870],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3261,21873,21875],{"className":3263,"code":21874,"language":71,"meta":3265,"style":3265},"pocet_clenu \u003C- c(1, 2, 3, 4, 5, 6)\ntydenni_vydaje \u003C- c(490, 820, 1230, 1570, 1950, 2320)\nmodel \u003C- lm(tydenni_vydaje ~ pocet_clenu)\nsummary(model)\n",[1434,21876,21877,21912,21953,21974],{"__ignoreMap":3265},[1115,21878,21879,21882,21884,21886,21888,21890,21892,21894,21896,21898,21900,21902,21904,21906,21908,21910],{"class":3270,"line":10},[1115,21880,21881],{"class":3280},"pocet_clenu",[1115,21883,3291],{"class":3273},[1115,21885,4142],{"class":3294},[1115,21887,1151],{"class":3277},[1115,21889,1921],{"class":3312},[1115,21891,1164],{"class":3273},[1115,21893,4156],{"class":3312},[1115,21895,1164],{"class":3273},[1115,21897,4197],{"class":3312},[1115,21899,1164],{"class":3273},[1115,21901,4184],{"class":3312},[1115,21903,1164],{"class":3273},[1115,21905,4161],{"class":3312},[1115,21907,1164],{"class":3273},[1115,21909,4171],{"class":3312},[1115,21911,3283],{"class":3277},[1115,21913,21914,21917,21919,21921,21923,21926,21928,21931,21933,21936,21938,21941,21943,21946,21948,21951],{"class":3270,"line":27},[1115,21915,21916],{"class":3280},"tydenni_vydaje",[1115,21918,3291],{"class":3273},[1115,21920,4142],{"class":3294},[1115,21922,1151],{"class":3277},[1115,21924,21925],{"class":3312},"490",[1115,21927,1164],{"class":3273},[1115,21929,21930],{"class":3312}," 820",[1115,21932,1164],{"class":3273},[1115,21934,21935],{"class":3312}," 1230",[1115,21937,1164],{"class":3273},[1115,21939,21940],{"class":3312}," 1570",[1115,21942,1164],{"class":3273},[1115,21944,21945],{"class":3312}," 1950",[1115,21947,1164],{"class":3273},[1115,21949,21950],{"class":3312}," 2320",[1115,21952,3283],{"class":3277},[1115,21954,21955,21957,21959,21962,21964,21966,21969,21972],{"class":3270,"line":148},[1115,21956,786],{"class":3280},[1115,21958,3291],{"class":3273},[1115,21960,21961],{"class":3294}," lm",[1115,21963,1151],{"class":3277},[1115,21965,21916],{"class":3280},[1115,21967,21968],{"class":3273}," ~",[1115,21970,21971],{"class":3280}," pocet_clenu",[1115,21973,3283],{"class":3277},[1115,21975,21976,21978,21980,21982],{"class":3270,"line":111},[1115,21977,4267],{"class":3294},[1115,21979,1151],{"class":3277},[1115,21981,786],{"class":3280},[1115,21983,3283],{"class":3277},[3261,21985,21988],{"className":21986,"code":21987,"language":4279,"meta":3265},[4277],"Call:\nlm(formula = tydenni_vydaje ~ pocet_clenu)\n\nResiduals:\n      1       2       3       4       5       6 \n 13.333 -24.667  17.333 -10.667   1.333   3.333 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept)  108.667     16.214   6.702  0.00258 ** \npocet_clenu  368.000      4.163  88.391 9.82e-08 ***\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 17.42 on 4 degrees of freedom\nMultiple R-squared:  0.9995,    Adjusted R-squared:  0.9994 \nF-statistic:  7813 on 1 and 4 DF,  p-value: 9.821e-08\n",[1434,21989,21987],{"__ignoreMap":3265},[1110,21991,21992,21993,22025,22026,22029,22030,22060,22061,22091,22092,22095,22096,22119],{},"Odhadnutý model je ",[1115,21994,21996],{"className":21995},[1136],[1138,21997,21998],{"xmlns":1140},[1142,21999,22000,22022],{},[1145,22001,22002,22008,22010,22013,22015,22018,22020],{},[1153,22003,22004,22006],{"accent":1121},[1156,22005,12274],{},[1148,22007,6165],{},[1148,22009,1914],{},[1919,22011,22012],{},"108,7",[1148,22014,5066],{},[1919,22016,22017],{},"368,0",[5009,22019,5011],{},[1156,22021,1158],{},[1172,22023,22024],{"encoding":1174},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[1434,22027,22028],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,22031,22033],{"className":22032},[1136],[1138,22034,22035],{"xmlns":1140},[1142,22036,22037,22057],{},[1145,22038,22039,22045,22047,22053,22055],{},[1217,22040,22041,22043],{},[1156,22042,6797],{},[1919,22044,2780],{},[1148,22046,2529],{},[1217,22048,22049,22051],{},[1156,22050,21449],{},[1156,22052,1223],{},[1148,22054,1914],{},[1919,22056,2780],{},[1172,22058,22059],{"encoding":1174},"H_0:\\beta_i=0"," proti ",[1115,22062,22064],{"className":22063},[1136],[1138,22065,22066],{"xmlns":1140},[1142,22067,22068,22088],{},[1145,22069,22070,22076,22078,22084,22086],{},[1217,22071,22072,22074],{},[1156,22073,6797],{},[1919,22075,1921],{},[1148,22077,2529],{},[1217,22079,22080,22082],{},[1156,22081,21449],{},[1156,22083,1223],{},[1148,22085,16087],{"mathvariant":2014},[1919,22087,2780],{},[1172,22089,22090],{"encoding":1174},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[1434,22093,22094],{},"Multiple R-squared"," je index determinace ",[1115,22097,22099],{"className":22098},[1136],[1138,22100,22101],{"xmlns":1140},[1142,22102,22103,22116],{},[1145,22104,22105,22111,22113],{},[5465,22106,22107,22109],{},[1156,22108,1167],{},[1919,22110,2302],{},[1148,22112,1914],{},[1919,22114,22115],{},"0,9995",[1172,22117,22118],{"encoding":1174},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,22121,22122],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3261,22124,22126],{"className":3263,"code":22125,"language":71,"meta":3265,"style":3265},"coef(model)\nfitted(model)\nresiduals(model)\n",[1434,22127,22128,22139,22150],{"__ignoreMap":3265},[1115,22129,22130,22133,22135,22137],{"class":3270,"line":10},[1115,22131,22132],{"class":3294},"coef",[1115,22134,1151],{"class":3277},[1115,22136,786],{"class":3280},[1115,22138,3283],{"class":3277},[1115,22140,22141,22144,22146,22148],{"class":3270,"line":27},[1115,22142,22143],{"class":3294},"fitted",[1115,22145,1151],{"class":3277},[1115,22147,786],{"class":3280},[1115,22149,3283],{"class":3277},[1115,22151,22152,22155,22157,22159],{"class":3270,"line":148},[1115,22153,22154],{"class":3294},"residuals",[1115,22156,1151],{"class":3277},[1115,22158,786],{"class":3280},[1115,22160,3283],{"class":3277},[3261,22162,22165],{"className":22163,"code":22164,"language":4279,"meta":3265},[4277],"(Intercept) pocet_clenu \n   108.6667    368.0000 \n        1         2         3         4         5         6 \n 476.6667  844.6667 1212.6667 1580.6667 1948.6667 2316.6667 \n         1          2          3          4          5          6 \n 13.333333 -24.666667  17.333333 -10.666667   1.333333   3.333333 \n",[1434,22166,22164],{"__ignoreMap":3265},[1110,22168,22169,22172,22173,1176,22199,22202,22203,22225,22226,1176,22243,22246,22247,22284],{},[1434,22170,22171],{},"coef()"," vrací odhadnuté parametry ",[1115,22174,22176],{"className":22175},[1136],[1138,22177,22178],{"xmlns":1140},[1142,22179,22180,22196],{},[1145,22181,22182,22188,22190],{},[1217,22183,22184,22186],{},[1156,22185,16632],{},[1919,22187,2780],{},[1148,22189,1164],{"separator":1121},[1217,22191,22192,22194],{},[1156,22193,16632],{},[1919,22195,1921],{},[1172,22197,22198],{"encoding":1174},"b_0,b_1",[1434,22200,22201],{},"fitted()"," predikce ",[1115,22204,22206],{"className":22205},[1136],[1138,22207,22208],{"xmlns":1140},[1142,22209,22210,22222],{},[1145,22211,22212],{},[1217,22213,22214,22220],{},[1153,22215,22216,22218],{"accent":1121},[1156,22217,12274],{},[1148,22219,6165],{},[1156,22221,1223],{},[1172,22223,22224],{"encoding":1174},"\\hat y_i"," pro pozorované ",[1115,22227,22229],{"className":22228},[1136],[1138,22230,22231],{"xmlns":1140},[1142,22232,22233,22241],{},[1145,22234,22235],{},[1217,22236,22237,22239],{},[1156,22238,1158],{},[1156,22240,1223],{},[1172,22242,3767],{"encoding":1174},[1434,22244,22245],{},"residuals()"," rezidua ",[1115,22248,22250],{"className":22249},[1136],[1138,22251,22252],{"xmlns":1140},[1142,22253,22254,22282],{},[1145,22255,22256,22262,22264,22270,22272],{},[1217,22257,22258,22260],{},[1156,22259,13735],{},[1156,22261,1223],{},[1148,22263,1914],{},[1217,22265,22266,22268],{},[1156,22267,12274],{},[1156,22269,1223],{},[1148,22271,1990],{},[1217,22273,22274,22280],{},[1153,22275,22276,22278],{"accent":1121},[1156,22277,12274],{},[1148,22279,6165],{},[1156,22281,1223],{},[1172,22283,21631],{"encoding":1174}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,22286,22287,22288,22301],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,22289,22291],{"className":22290},[1136],[1138,22292,22293],{"xmlns":1140},[1142,22294,22295,22299],{},[1145,22296,22297],{},[1156,22298,1158],{},[1172,22300,1158],{"encoding":1174}," (zde 7 a 8 členů domácnosti):",[3261,22303,22305],{"className":3263,"code":22304,"language":71,"meta":3265,"style":3265},"confint(model, level = 0.95)\nnove \u003C- data.frame(pocet_clenu = c(7, 8))\npredict(model, newdata = nove, interval = \"confidence\", level = 0.95)\npredict(model, newdata = nove, interval = \"prediction\", level = 0.95)\n",[1434,22306,22307,22327,22355,22394],{"__ignoreMap":3265},[1115,22308,22309,22312,22314,22316,22318,22321,22323,22325],{"class":3270,"line":10},[1115,22310,22311],{"class":3294},"confint",[1115,22313,1151],{"class":3277},[1115,22315,786],{"class":3280},[1115,22317,1164],{"class":3273},[1115,22319,22320],{"class":3280}," level",[1115,22322,3309],{"class":3273},[1115,22324,15134],{"class":3312},[1115,22326,3283],{"class":3277},[1115,22328,22329,22332,22334,22337,22339,22341,22343,22345,22347,22349,22351,22353],{"class":3270,"line":27},[1115,22330,22331],{"class":3280},"nove",[1115,22333,3291],{"class":3273},[1115,22335,22336],{"class":3294}," data.frame",[1115,22338,1151],{"class":3277},[1115,22340,21881],{"class":3280},[1115,22342,3309],{"class":3273},[1115,22344,4142],{"class":3294},[1115,22346,1151],{"class":3277},[1115,22348,4147],{"class":3312},[1115,22350,1164],{"class":3273},[1115,22352,20368],{"class":3312},[1115,22354,6019],{"class":3277},[1115,22356,22357,22360,22362,22364,22366,22369,22371,22374,22376,22379,22381,22384,22386,22388,22390,22392],{"class":3270,"line":148},[1115,22358,22359],{"class":3294},"predict",[1115,22361,1151],{"class":3277},[1115,22363,786],{"class":3280},[1115,22365,1164],{"class":3273},[1115,22367,22368],{"class":3280}," newdata",[1115,22370,3309],{"class":3273},[1115,22372,22373],{"class":3280}," nove",[1115,22375,1164],{"class":3273},[1115,22377,22378],{"class":3280}," interval",[1115,22380,3309],{"class":3273},[1115,22382,22383],{"class":3300}," \"confidence\"",[1115,22385,1164],{"class":3273},[1115,22387,22320],{"class":3280},[1115,22389,3309],{"class":3273},[1115,22391,15134],{"class":3312},[1115,22393,3283],{"class":3277},[1115,22395,22396,22398,22400,22402,22404,22406,22408,22410,22412,22414,22416,22419,22421,22423,22425,22427],{"class":3270,"line":111},[1115,22397,22359],{"class":3294},[1115,22399,1151],{"class":3277},[1115,22401,786],{"class":3280},[1115,22403,1164],{"class":3273},[1115,22405,22368],{"class":3280},[1115,22407,3309],{"class":3273},[1115,22409,22373],{"class":3280},[1115,22411,1164],{"class":3273},[1115,22413,22378],{"class":3280},[1115,22415,3309],{"class":3273},[1115,22417,22418],{"class":3300}," \"prediction\"",[1115,22420,1164],{"class":3273},[1115,22422,22320],{"class":3280},[1115,22424,3309],{"class":3273},[1115,22426,15134],{"class":3312},[1115,22428,3283],{"class":3277},[3261,22430,22433],{"className":22431,"code":22432,"language":4279,"meta":3265},[4277],"                2.5 %   97.5 %\n(Intercept)  63.64981 153.6835\npocet_clenu 356.44074 379.5593\n       fit     lwr      upr\n1 2684.667 2639.65 2729.684\n2 3052.667 2997.03 3108.303\n       fit      lwr      upr\n1 2684.667 2618.600 2750.733\n2 3052.667 2978.953 3126.381\n",[1434,22434,22432],{"__ignoreMap":3265},[1110,22436,22437,22440,22441,6884,22444,22457,22458,1176,22471,22474,22475,22478],{},[1434,22438,22439],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1445,22442,22443],{},"střední hodnotu",[1115,22445,22447],{"className":22446},[1136],[1138,22448,22449],{"xmlns":1140},[1142,22450,22451,22455],{},[1145,22452,22453],{},[1156,22454,12274],{},[1172,22456,12274],{"encoding":1174}," při daném ",[1115,22459,22461],{"className":22460},[1136],[1138,22462,22463],{"xmlns":1140},[1142,22464,22465,22469],{},[1145,22466,22467],{},[1156,22468,1158],{},[1172,22470,1158],{"encoding":1174},[1434,22472,22473],{},"interval = \"prediction\""," širší interval pro ",[1445,22476,22477],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[1818,22480,22482],{"id":22481},"diagnostika-modelu","Diagnostika modelu",[1110,22484,22485,22486,1176,22489,1204,22492,22495],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1445,22487,22488],{},"absenci autokorelace",[1445,22490,22491],{},"stálosti rozptylu (homoskedasticitě)",[1445,22493,22494],{},"normalitě",". V R se ověřují takto:",[3261,22497,22499],{"className":3263,"code":22498,"language":71,"meta":3265,"style":3265},"library(lmtest)\ndwtest(model)\n",[1434,22500,22501,22512],{"__ignoreMap":3265},[1115,22502,22503,22505,22507,22510],{"class":3270,"line":10},[1115,22504,3274],{"class":3273},[1115,22506,1151],{"class":3277},[1115,22508,22509],{"class":3280},"lmtest",[1115,22511,3283],{"class":3277},[1115,22513,22514,22517,22519,22521],{"class":3270,"line":27},[1115,22515,22516],{"class":3294},"dwtest",[1115,22518,1151],{"class":3277},[1115,22520,786],{"class":3280},[1115,22522,3283],{"class":3277},[3261,22524,22527],{"className":22525,"code":22526,"language":4279,"meta":3265},[4277],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[1434,22528,22526],{"__ignoreMap":3265},[1110,22530,22531,22532,22549,22550,22567,22568,22585],{},"Durbinův–Watsonův test má ",[1115,22533,22535],{"className":22534},[1136],[1138,22536,22537],{"xmlns":1140},[1142,22538,22539,22547],{},[1145,22540,22541],{},[1217,22542,22543,22545],{},[1156,22544,6797],{},[1919,22546,2780],{},[1172,22548,6802],{"encoding":1174},": v modelu není problém s autokorelací, proti ",[1115,22551,22553],{"className":22552},[1136],[1138,22554,22555],{"xmlns":1140},[1142,22556,22557,22565],{},[1145,22558,22559],{},[1217,22560,22561,22563],{},[1156,22562,6797],{},[1919,22564,1921],{},[1172,22566,8200],{"encoding":1174},": v modelu problém s autokorelací je. Statistika DW se pohybuje mezi 0 a 4, hodnota blízko 2 znamená žádnou autokorelaci. Zde p-hodnota 0,96 je výrazně nad 0,05, ",[1115,22569,22571],{"className":22570},[1136],[1138,22572,22573],{"xmlns":1140},[1142,22574,22575,22583],{},[1145,22576,22577],{},[1217,22578,22579,22581],{},[1156,22580,6797],{},[1919,22582,2780],{},[1172,22584,6802],{"encoding":1174}," se nezamítá.",[3261,22587,22589],{"className":3263,"code":22588,"language":71,"meta":3265,"style":3265},"library(whitestrap)\nwhite_test(model)\n",[1434,22590,22591,22602],{"__ignoreMap":3265},[1115,22592,22593,22595,22597,22600],{"class":3270,"line":10},[1115,22594,3274],{"class":3273},[1115,22596,1151],{"class":3277},[1115,22598,22599],{"class":3280},"whitestrap",[1115,22601,3283],{"class":3277},[1115,22603,22604,22607,22609,22611],{"class":3270,"line":27},[1115,22605,22606],{"class":3294},"white_test",[1115,22608,1151],{"class":3277},[1115,22610,786],{"class":3280},[1115,22612,3283],{"class":3277},[3261,22614,22617],{"className":22615,"code":22616,"language":4279,"meta":3265},[4277],"White's test results\n\nNull hypothesis: Homoskedasticity of the residuals\nAlternative hypothesis: Heteroskedasticity of the residuals\nTest Statistic: 3.14\nP-value: 0.207817\n",[1434,22618,22616],{"__ignoreMap":3265},[1110,22620,22621,22622,22639,22640,22657,22658,22585],{},"Whiteův test má ",[1115,22623,22625],{"className":22624},[1136],[1138,22626,22627],{"xmlns":1140},[1142,22628,22629,22637],{},[1145,22630,22631],{},[1217,22632,22633,22635],{},[1156,22634,6797],{},[1919,22636,2780],{},[1172,22638,6802],{"encoding":1174},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,22641,22643],{"className":22642},[1136],[1138,22644,22645],{"xmlns":1140},[1142,22646,22647,22655],{},[1145,22648,22649],{},[1217,22650,22651,22653],{},[1156,22652,6797],{},[1919,22654,1921],{},[1172,22656,8200],{"encoding":1174},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,22659,22661],{"className":22660},[1136],[1138,22662,22663],{"xmlns":1140},[1142,22664,22665,22673],{},[1145,22666,22667],{},[1217,22668,22669,22671],{},[1156,22670,6797],{},[1919,22672,2780],{},[1172,22674,6802],{"encoding":1174},[3261,22676,22678],{"className":3263,"code":22677,"language":71,"meta":3265,"style":3265},"shapiro.test(residuals(model))\n",[1434,22679,22680],{"__ignoreMap":3265},[1115,22681,22682,22685,22687,22689,22691,22693],{"class":3270,"line":10},[1115,22683,22684],{"class":3294},"shapiro.test",[1115,22686,1151],{"class":3277},[1115,22688,22154],{"class":3294},[1115,22690,1151],{"class":3277},[1115,22692,786],{"class":3280},[1115,22694,6019],{"class":3277},[3261,22696,22699],{"className":22697,"code":22698,"language":4279,"meta":3265},[4277],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[1434,22700,22698],{"__ignoreMap":3265},[1110,22702,22703,22704,22721],{},"Shapiro–Wilkův test má ",[1115,22705,22707],{"className":22706},[1136],[1138,22708,22709],{"xmlns":1140},[1142,22710,22711,22719],{},[1145,22712,22713],{},[1217,22714,22715,22717],{},[1156,22716,6797],{},[1919,22718,2780],{},[1172,22720,6802],{"encoding":1174},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,22723,22724],{},[1527,22725],{"alt":22726,"className":22727,"src":22728},"mask-ra-diagnostika-rezidui",[1531,1532],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,22730,22731],{},"Grafická kontrola normality doplňuje Shapiro–Wilkův test: body v levém panelu by měly být rovnoměrně rozptýlené po obou stranách vodorovné osy (bez trychtýře či oblouku), body v Q-Q grafu by měly ležet kolem přímky. U malého počtu pozorování se dává přednost testu; u velkého datového souboru se předpoklad normality reziduí stává méně kritickým díky centrální limitní větě.",[1103,22733,22735,22742,22773,22808,22873],{"className":22734,"dataCallout":2145},[1106,2144],[1110,22736,22738,22741],{"className":22737},[1113],[1115,22739],{"className":22740,"ariaHidden":1121},[1118,2152,1120],"Příklad: Regresní přímka",[1110,22743,22744,22745,22758,22759,22772],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,22746,22748],{"className":22747},[1136],[1138,22749,22750],{"xmlns":1140},[1142,22751,22752,22756],{},[1145,22753,22754],{},[1156,22755,12274],{},[1172,22757,12274],{"encoding":1174},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,22760,22762],{"className":22761},[1136],[1138,22763,22764],{"xmlns":1140},[1142,22765,22766,22770],{},[1145,22767,22768],{},[1156,22769,1158],{},[1172,22771,1158],{"encoding":1174},") za rok 2015 u dvanácti vybraných soukromých firem s více než 30 zaměstnanci byla metodou nejmenších čtverců odhadnuta regresní přímka modelující závislost hodnoty produkce na výši investic.",[1110,22774,22775,22776,1247],{},"Výsledek: ",[1115,22777,22779],{"className":22778},[1136],[1138,22780,22781],{"xmlns":1140},[1142,22782,22783,22805],{},[1145,22784,22785,22791,22793,22796,22798,22801,22803],{},[1153,22786,22787,22789],{"accent":1121},[1156,22788,12274],{},[1148,22790,6165],{},[1148,22792,1914],{},[1919,22794,22795],{},"32,74",[1148,22797,5066],{},[1919,22799,22800],{},"2,15",[5009,22802,5011],{},[1156,22804,1158],{},[1172,22806,22807],{"encoding":1174},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,22809,21809,22810,22832,22833,22872],{},[1115,22811,22813],{"className":22812},[1136],[1138,22814,22815],{"xmlns":1140},[1142,22816,22817,22829],{},[1145,22818,22819,22825,22827],{},[1217,22820,22821,22823],{},[1156,22822,16632],{},[1919,22824,1921],{},[1148,22826,1914],{},[1919,22828,22800],{},[1172,22830,22831],{"encoding":1174},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,22834,22836],{"className":22835},[1136],[1138,22837,22838],{"xmlns":1140},[1142,22839,22840,22869],{},[1145,22841,22842,22844,22846,22848,22850,22852,22854,22856,22858,22860,22862,22865,22867],{},[1919,22843,22800],{},[1148,22845,13255],{},[1919,22847,1921],{},[5009,22849,5011],{},[1919,22851,16451],{},[5009,22853,5011],{},[1919,22855,16451],{},[1148,22857,1914],{},[1919,22859,2302],{},[5009,22861,5011],{},[1919,22863,22864],{},"150",[5009,22866,5011],{},[1919,22868,16451],{},[1172,22870,22871],{"encoding":1174},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,22874,22875,22876,4984,22895,22943,22944,21205],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,22877,22879],{"className":22878},[1136],[1138,22880,22881],{"xmlns":1140},[1142,22882,22883,22892],{},[1145,22884,22885,22887,22889],{},[1156,22886,1158],{},[1148,22888,1914],{},[1919,22890,22891],{},"34",[1172,22893,22894],{"encoding":1174},"x=34",[1115,22896,22898],{"className":22897},[1136],[1138,22899,22900],{"xmlns":1140},[1142,22901,22902,22940],{},[1145,22903,22904,22914,22916,22922,22924,22930,22932,22934,22937],{},[1217,22905,22906,22912],{},[1153,22907,22908,22910],{"accent":1121},[1156,22909,12274],{},[1148,22911,6165],{},[1919,22913,2671],{},[1148,22915,1914],{},[1217,22917,22918,22920],{},[1156,22919,16632],{},[1919,22921,2780],{},[1148,22923,5066],{},[1217,22925,22926,22928],{},[1156,22927,16632],{},[1919,22929,1921],{},[1148,22931,13255],{},[1919,22933,22891],{},[1148,22935,22936],{},"≐",[1919,22938,22939],{},"105,81",[1172,22941,22942],{"encoding":1174},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,22945,22947],{"className":22946},[1136],[1138,22948,22949],{"xmlns":1140},[1142,22950,22951,22968],{},[1145,22952,22953,22955,22957,22959,22961,22963,22965],{},[1919,22954,22795],{},[1148,22956,5066],{},[1919,22958,22800],{},[1148,22960,13255],{},[1919,22962,22891],{},[1148,22964,22936],{},[1919,22966,22967],{},"105,8",[1172,22969,22970],{"encoding":1174},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1437,22972,22974],{"id":22973},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,22976,22977,22978,22981,22982,23049,23050,23068,23069,23086],{},"Když přímka závislost nevystihuje, nabízí se další ",[1445,22979,22980],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,22983,22985],{"className":22984},[1136],[1138,22986,22987],{"xmlns":1140},[1142,22988,22989,23046],{},[1145,22990,22991,22993,22995,23001,23003,23009,23015,23017,23019,23021,23023,23026,23028,23034,23040,23042,23044],{},[1156,22992,21434],{},[1148,22994,1914],{},[1217,22996,22997,22999],{},[1156,22998,21449],{},[1919,23000,2780],{},[1148,23002,5066],{},[1217,23004,23005,23007],{},[1156,23006,21449],{},[1919,23008,1921],{},[1217,23010,23011,23013],{},[1156,23012,11920],{},[1919,23014,1921],{},[1148,23016,1151],{"stretchy":1150},[1156,23018,1158],{},[1148,23020,1170],{"stretchy":1150},[1148,23022,5066],{},[1148,23024,23025],{},"⋯",[1148,23027,5066],{},[1217,23029,23030,23032],{},[1156,23031,21449],{},[1156,23033,1110],{},[1217,23035,23036,23038],{},[1156,23037,11920],{},[1156,23039,1110],{},[1148,23041,1151],{"stretchy":1150},[1156,23043,1158],{},[1148,23045,1170],{"stretchy":1150},[1172,23047,23048],{"encoding":1174},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,23051,23053],{"className":23052},[1136],[1138,23054,23055],{"xmlns":1140},[1142,23056,23057,23065],{},[1145,23058,23059],{},[1217,23060,23061,23063],{},[1156,23062,11920],{},[1156,23064,1223],{},[1172,23066,23067],{"encoding":1174},"f_i"," a neznámými parametry ",[1115,23070,23072],{"className":23071},[1136],[1138,23073,23074],{"xmlns":1140},[1142,23075,23076,23084],{},[1145,23077,23078],{},[1217,23079,23080,23082],{},[1156,23081,21449],{},[1156,23083,1223],{},[1172,23085,21495],{"encoding":1174},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,23088,23090],{"className":23089},[1136],[1138,23091,23092],{"xmlns":1140,"display":1897},[1142,23093,23094,23403],{},[23095,23096,23099,23171,23284,23343],"mtable",{"rowspacing":23097,"columnalign":23098,"columnspacing":11908},"0.25em","right left",[23100,23101,23102,23125],"mtr",{},[23103,23104,23105],"mtd",{},[4995,23106,23107],{"scriptlevel":2780,"displaystyle":1121},[1145,23108,23109,23123],{},[1145,23110,23111,23114,23120],{},[5009,23112,23113],{},"parabolick",[1153,23115,23116,23118],{"accent":1121},[5009,23117,6613],{},[1148,23119,16629],{},[5009,23121,23122],{}," regrese: ",[1954,23124],{"width":3663},[23103,23126,23127],{},[4995,23128,23129],{"scriptlevel":2780,"displaystyle":1121},[1145,23130,23131,23133,23139,23141,23147,23149,23155,23157,23159,23165],{},[1145,23132],{},[1153,23134,23135,23137],{"accent":1121},[1156,23136,12274],{},[1148,23138,6165],{},[1148,23140,1914],{},[1217,23142,23143,23145],{},[1156,23144,16632],{},[1919,23146,2780],{},[1148,23148,5066],{},[1217,23150,23151,23153],{},[1156,23152,16632],{},[1919,23154,1921],{},[1156,23156,1158],{},[1148,23158,5066],{},[1217,23160,23161,23163],{},[1156,23162,16632],{},[1919,23164,2302],{},[5465,23166,23167,23169],{},[1156,23168,1158],{},[1919,23170,2302],{},[23100,23172,23173,23220],{},[23103,23174,23175],{},[4995,23176,23177],{"scriptlevel":2780,"displaystyle":1121},[1145,23178,23179,23218],{},[1145,23180,23181,23184,23190,23193,23197,23200,23206,23209,23215],{},[5009,23182,23183],{},"polynomick",[1153,23185,23186,23188],{"accent":1121},[5009,23187,6613],{},[1148,23189,16629],{},[5009,23191,23192],{}," regrese ",[4995,23194,23195],{"scriptlevel":2780,"displaystyle":1150},[1156,23196,1110],{},[5009,23198,23199],{},"-t",[1153,23201,23202,23204],{"accent":1121},[5009,23203,13735],{},[1148,23205,16629],{},[5009,23207,23208],{},"ho stupn",[1153,23210,23211,23213],{"accent":1121},[5009,23212,13735],{},[1148,23214,16639],{},[5009,23216,23217],{},": ",[1954,23219],{"width":3663},[23103,23221,23222],{},[4995,23223,23224],{"scriptlevel":2780,"displaystyle":1121},[1145,23225,23226,23228,23234,23236,23242,23244,23250,23252,23254,23260,23266,23268,23270,23272,23278],{},[1145,23227],{},[1153,23229,23230,23232],{"accent":1121},[1156,23231,12274],{},[1148,23233,6165],{},[1148,23235,1914],{},[1217,23237,23238,23240],{},[1156,23239,16632],{},[1919,23241,2780],{},[1148,23243,5066],{},[1217,23245,23246,23248],{},[1156,23247,16632],{},[1919,23249,1921],{},[1156,23251,1158],{},[1148,23253,5066],{},[1217,23255,23256,23258],{},[1156,23257,16632],{},[1919,23259,2302],{},[5465,23261,23262,23264],{},[1156,23263,1158],{},[1919,23265,2302],{},[1148,23267,5066],{},[1148,23269,23025],{},[1148,23271,5066],{},[1217,23273,23274,23276],{},[1156,23275,16632],{},[1156,23277,1110],{},[5465,23279,23280,23282],{},[1156,23281,1158],{},[1156,23283,1110],{},[23100,23285,23286,23307],{},[23103,23287,23288],{},[4995,23289,23290],{"scriptlevel":2780,"displaystyle":1121},[1145,23291,23292,23305],{},[1145,23293,23294,23297,23303],{},[5009,23295,23296],{},"hyperbolick",[1153,23298,23299,23301],{"accent":1121},[5009,23300,6613],{},[1148,23302,16629],{},[5009,23304,23122],{},[1954,23306],{"width":3663},[23103,23308,23309],{},[4995,23310,23311],{"scriptlevel":2780,"displaystyle":1121},[1145,23312,23313,23315,23321,23323,23329,23331,23337],{},[1145,23314],{},[1153,23316,23317,23319],{"accent":1121},[1156,23318,12274],{},[1148,23320,6165],{},[1148,23322,1914],{},[1217,23324,23325,23327],{},[1156,23326,16632],{},[1919,23328,2780],{},[1148,23330,5066],{},[1217,23332,23333,23335],{},[1156,23334,16632],{},[1919,23336,1921],{},[1916,23338,23339,23341],{},[1919,23340,1921],{},[1156,23342,1158],{},[23100,23344,23345,23366],{},[23103,23346,23347],{},[4995,23348,23349],{"scriptlevel":2780,"displaystyle":1121},[1145,23350,23351,23364],{},[1145,23352,23353,23356,23362],{},[5009,23354,23355],{},"logaritmick",[1153,23357,23358,23360],{"accent":1121},[5009,23359,6613],{},[1148,23361,16629],{},[5009,23363,23122],{},[1954,23365],{"width":3663},[23103,23367,23368],{},[4995,23369,23370],{"scriptlevel":2780,"displaystyle":1121},[1145,23371,23372,23374,23380,23382,23388,23390,23396,23399,23401],{},[1145,23373],{},[1153,23375,23376,23378],{"accent":1121},[1156,23377,12274],{},[1148,23379,6165],{},[1148,23381,1914],{},[1217,23383,23384,23386],{},[1156,23385,16632],{},[1919,23387,2780],{},[1148,23389,5066],{},[1217,23391,23392,23394],{},[1156,23393,16632],{},[1919,23395,1921],{},[1156,23397,23398],{},"ln",[1148,23400,1975],{},[1156,23402,1158],{},[1172,23404,23405],{"encoding":1174},"\\begin{aligned}\n\\text{parabolická regrese: }\\quad &\\hat y = b_0 + b_1 x + b_2 x^2\\\\\n\\text{polynomická regrese $p$-tého stupně: }\\quad &\\hat y = b_0 + b_1 x + b_2 x^2 + \\dots + b_p x^p\\\\\n\\text{hyperbolická regrese: }\\quad &\\hat y = b_0 + b_1\\frac1x\\\\\n\\text{logaritmická regrese: }\\quad &\\hat y = b_0 + b_1\\ln x\n\\end{aligned}",[1110,23407,23408,23409,23412,23413,23459,23460,2529],{},"Naproti tomu ",[1445,23410,23411],{},"nelineární funkce"," nelze do tvaru ",[1115,23414,23416],{"className":23415},[1136],[1138,23417,23418],{"xmlns":1140},[1142,23419,23420,23456],{},[1145,23421,23422,23424,23426,23432,23434,23440,23446,23448,23450,23452,23454],{},[1156,23423,21434],{},[1148,23425,1914],{},[1217,23427,23428,23430],{},[1156,23429,21449],{},[1919,23431,2780],{},[1148,23433,5066],{},[1217,23435,23436,23438],{},[1156,23437,21449],{},[1919,23439,1921],{},[1217,23441,23442,23444],{},[1156,23443,11920],{},[1919,23445,1921],{},[1148,23447,1151],{"stretchy":1150},[1156,23449,1158],{},[1148,23451,1170],{"stretchy":1150},[1148,23453,5066],{},[1148,23455,2043],{},[1172,23457,23458],{"encoding":1174},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots"," převést — je nelineární i ve svých parametrech. Jejich parametry nelze získat přímo metodou nejmenších čtverců, ale vhodnou transformací nebo iterativně. Základní příklad je ",[1445,23461,23462],{},"exponenciální regrese",[1115,23464,23466],{"className":23465},[1136],[1138,23467,23468],{"xmlns":1140,"display":1897},[1142,23469,23470,23502],{},[1145,23471,23472,23478,23480,23486,23488,23500],{},[1153,23473,23474,23476],{"accent":1121},[1156,23475,12274],{},[1148,23477,6165],{},[1148,23479,1914],{},[1217,23481,23482,23484],{},[1156,23483,16632],{},[1919,23485,2780],{},[1148,23487,13255],{},[8555,23489,23490,23492,23494],{},[1156,23491,16632],{},[1919,23493,1921],{},[1145,23495,23496,23498],{},[5009,23497,5011],{},[1156,23499,1158],{},[1156,23501,1247],{"mathvariant":2014},[1172,23503,23504],{"encoding":1174},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,23506,23507],{},[1527,23508],{"alt":23509,"className":23510,"src":23511},"mask-ra-nelinearni-krivky",[1531,1532],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[1818,23513,23515],{"id":23514},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,23517,23518,23519,2529],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[1434,23520,23521],{},"I(x^2)",[3261,23523,23525],{"className":3263,"code":23524,"language":71,"meta":3265,"style":3265},"rok \u003C- c(1, 2, 3, 4, 5, 6)\nzisk \u003C- c(112, 149, 238, 354, 580, 867)\nmodel_parabola \u003C- lm(zisk ~ rok + I(rok^2))\nsummary(model_parabola)\n",[1434,23526,23527,23562,23602,23635],{"__ignoreMap":3265},[1115,23528,23529,23532,23534,23536,23538,23540,23542,23544,23546,23548,23550,23552,23554,23556,23558,23560],{"class":3270,"line":10},[1115,23530,23531],{"class":3280},"rok",[1115,23533,3291],{"class":3273},[1115,23535,4142],{"class":3294},[1115,23537,1151],{"class":3277},[1115,23539,1921],{"class":3312},[1115,23541,1164],{"class":3273},[1115,23543,4156],{"class":3312},[1115,23545,1164],{"class":3273},[1115,23547,4197],{"class":3312},[1115,23549,1164],{"class":3273},[1115,23551,4184],{"class":3312},[1115,23553,1164],{"class":3273},[1115,23555,4161],{"class":3312},[1115,23557,1164],{"class":3273},[1115,23559,4171],{"class":3312},[1115,23561,3283],{"class":3277},[1115,23563,23564,23566,23568,23570,23572,23575,23577,23580,23582,23585,23587,23590,23592,23595,23597,23600],{"class":3270,"line":27},[1115,23565,1088],{"class":3280},[1115,23567,3291],{"class":3273},[1115,23569,4142],{"class":3294},[1115,23571,1151],{"class":3277},[1115,23573,23574],{"class":3312},"112",[1115,23576,1164],{"class":3273},[1115,23578,23579],{"class":3312}," 149",[1115,23581,1164],{"class":3273},[1115,23583,23584],{"class":3312}," 238",[1115,23586,1164],{"class":3273},[1115,23588,23589],{"class":3312}," 354",[1115,23591,1164],{"class":3273},[1115,23593,23594],{"class":3312}," 580",[1115,23596,1164],{"class":3273},[1115,23598,23599],{"class":3312}," 867",[1115,23601,3283],{"class":3277},[1115,23603,23604,23607,23609,23611,23613,23615,23617,23620,23622,23625,23627,23629,23631,23633],{"class":3270,"line":148},[1115,23605,23606],{"class":3280},"model_parabola",[1115,23608,3291],{"class":3273},[1115,23610,21961],{"class":3294},[1115,23612,1151],{"class":3277},[1115,23614,1088],{"class":3280},[1115,23616,21968],{"class":3273},[1115,23618,23619],{"class":3280}," rok",[1115,23621,6170],{"class":3273},[1115,23623,23624],{"class":3294}," I",[1115,23626,1151],{"class":3277},[1115,23628,23531],{"class":3280},[1115,23630,6165],{"class":3273},[1115,23632,2302],{"class":3312},[1115,23634,6019],{"class":3277},[1115,23636,23637,23639,23641,23643],{"class":3270,"line":111},[1115,23638,4267],{"class":3294},[1115,23640,1151],{"class":3277},[1115,23642,23606],{"class":3280},[1115,23644,3283],{"class":3277},[3261,23646,23649],{"className":23647,"code":23648,"language":4279,"meta":3265},[4277],"Call:\nlm(formula = zisk ~ rok + I(rok^2))\n\nResiduals:\n      1       2       3       4       5       6 \n -8.071   9.243  14.343 -17.771  -4.100   6.357 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)   \n(Intercept)  164.600     27.892   5.901  0.00972 **\nrok          -76.636     18.248  -4.200  0.02464 * \nI(rok^2)      32.107      2.552  12.582  0.00108 **\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 15.59 on 3 degrees of freedom\nMultiple R-squared:  0.9983,    Adjusted R-squared:  0.9971 \nF-statistic: 868.7 on 2 and 3 DF,  p-value: 7.156e-05\n",[1434,23650,23648],{"__ignoreMap":3265},[1110,23652,23653,23654,23699],{},"Odhadnutá parabola ",[1115,23655,23657],{"className":23656},[1136],[1138,23658,23659],{"xmlns":1140},[1142,23660,23661,23696],{},[1145,23662,23663,23669,23671,23674,23676,23679,23681,23683,23685,23688,23690],{},[1153,23664,23665,23667],{"accent":1121},[1156,23666,12274],{},[1148,23668,6165],{},[1148,23670,1914],{},[1919,23672,23673],{},"164,6",[1148,23675,1990],{},[1919,23677,23678],{},"76,6",[5009,23680,5011],{},[1156,23682,1158],{},[1148,23684,5066],{},[1919,23686,23687],{},"32,1",[5009,23689,5011],{},[5465,23691,23692,23694],{},[1156,23693,1158],{},[1919,23695,2302],{},[1172,23697,23698],{"encoding":1174},"\\hat y = 164{,}6 - 76{,}6\\,x + 32{,}1\\,x^2"," vysvětluje 99,8 % rozptylu zisku — podstatně víc, než by vysvětlila přímka proložená stejně rostoucími daty.",[1818,23701,23703],{"id":23702},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,23705,23706,23707,23709],{},"Nelineární funkce se v R odhadují funkcí ",[1434,23708,21220],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3261,23711,23713],{"className":3263,"code":23712,"language":71,"meta":3265,"style":3265},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[1434,23714,23715,23725,23760],{"__ignoreMap":3265},[1115,23716,23717,23719,23721,23723],{"class":3270,"line":10},[1115,23718,3274],{"class":3273},[1115,23720,1151],{"class":3277},[1115,23722,21204],{"class":3280},[1115,23724,3283],{"class":3277},[1115,23726,23727,23730,23732,23735,23737,23739,23741,23744,23746,23749,23751,23754,23756,23758],{"class":3270,"line":27},[1115,23728,23729],{"class":3280},"model_exp",[1115,23731,3291],{"class":3273},[1115,23733,23734],{"class":3294}," nls2",[1115,23736,1151],{"class":3277},[1115,23738,1088],{"class":3280},[1115,23740,21968],{"class":3273},[1115,23742,23743],{"class":3280}," b1",[1115,23745,6216],{"class":3273},[1115,23747,23748],{"class":3294}," exp",[1115,23750,1151],{"class":3277},[1115,23752,23753],{"class":3280},"b2",[1115,23755,6216],{"class":3273},[1115,23757,23619],{"class":3280},[1115,23759,6019],{"class":3277},[1115,23761,23762,23764,23766,23768],{"class":3270,"line":148},[1115,23763,4267],{"class":3294},[1115,23765,1151],{"class":3277},[1115,23767,23729],{"class":3280},[1115,23769,3283],{"class":3277},[3261,23771,23774],{"className":23772,"code":23773,"language":4279,"meta":3265},[4277],"Formula: zisk ~ b1 * exp(b2 * rok)\n\nParameters:\n   Estimate Std. Error t value Pr(>|t|)    \nb1 65.35423    3.57542   18.28 5.27e-05 ***\nb2  0.43161    0.01013   42.63 1.81e-06 ***\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 11.89 on 4 degrees of freedom\n",[1434,23775,23773],{"__ignoreMap":3265},[1110,23777,23778,23779,2529],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,23780,23782],{"className":23781},[1136],[1138,23783,23784],{"xmlns":1140},[1142,23785,23786,23812],{},[1145,23787,23788,23794,23796,23802,23804],{},[1153,23789,23790,23792],{"accent":1121},[1156,23791,12274],{},[1148,23793,6165],{},[1148,23795,1914],{},[1217,23797,23798,23800],{},[1156,23799,16632],{},[1919,23801,1921],{},[1148,23803,13255],{},[8555,23805,23806,23808,23810],{},[1156,23807,16632],{},[1919,23809,2302],{},[1156,23811,1158],{},[1172,23813,23814],{"encoding":1174},"\\hat y=b_1\\cdot b_2^{x}",[3261,23816,23818],{"className":3263,"code":23817,"language":71,"meta":3265,"style":3265},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[1434,23819,23820,23849],{"__ignoreMap":3265},[1115,23821,23822,23825,23827,23829,23831,23833,23835,23837,23839,23841,23843,23845,23847],{"class":3270,"line":10},[1115,23823,23824],{"class":3280},"model_pow",[1115,23826,3291],{"class":3273},[1115,23828,23734],{"class":3294},[1115,23830,1151],{"class":3277},[1115,23832,1088],{"class":3280},[1115,23834,21968],{"class":3273},[1115,23836,23743],{"class":3280},[1115,23838,6216],{"class":3273},[1115,23840,6173],{"class":3277},[1115,23842,23753],{"class":3280},[1115,23844,6165],{"class":3273},[1115,23846,23531],{"class":3280},[1115,23848,6019],{"class":3277},[1115,23850,23851,23853,23855,23857],{"class":3270,"line":27},[1115,23852,4267],{"class":3294},[1115,23854,1151],{"class":3277},[1115,23856,23824],{"class":3280},[1115,23858,3283],{"class":3277},[3261,23860,23863],{"className":23861,"code":23862,"language":4279,"meta":3265},[4277],"Formula: zisk ~ b1 * (b2^rok)\n\nParameters:\n   Estimate Std. Error t value Pr(>|t|)    \nb1 65.35424    3.57542   18.28 5.27e-05 ***\nb2  1.53973    0.01559   98.76 6.30e-08 ***\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 11.89 on 4 degrees of freedom\n",[1434,23864,23862],{"__ignoreMap":3265},[1110,23866,23867,23868,23932,23933,23957],{},"Obě varianty popisují stejnou křivku (",[1115,23869,23871],{"className":23870},[1136],[1138,23872,23873],{"xmlns":1140},[1142,23874,23875,23929],{},[1145,23876,23877,23894,23896],{},[8555,23878,23879,23881,23883],{},[1156,23880,16632],{},[1919,23882,2302],{},[1145,23884,23885,23888],{},[5009,23886,23887],{},"mocninn",[1153,23889,23890,23892],{"accent":1121},[5009,23891,12274],{},[1148,23893,16629],{},[1148,23895,1914],{},[5465,23897,23898,23900],{},[1156,23899,13735],{},[1145,23901,23902,23904],{},[5009,23903,5011],{},[8555,23905,23906,23908,23910],{},[1156,23907,16632],{},[1919,23909,2302],{},[1145,23911,23912,23915,23921,23923],{},[5009,23913,23914],{},"exponenci",[1153,23916,23917,23919],{"accent":1121},[5009,23918,6613],{},[1148,23920,16629],{},[5009,23922,23398],{},[1153,23924,23925,23927],{"accent":1121},[5009,23926,16877],{},[1148,23928,16629],{},[1172,23930,23931],{"encoding":1174},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,23934,23936],{"className":23935},[1136],[1138,23937,23938],{"xmlns":1140},[1142,23939,23940,23954],{},[1145,23941,23942,23949,23951],{},[5465,23943,23944,23946],{},[1156,23945,13735],{},[1919,23947,23948],{},"0,4316",[1148,23950,14579],{},[1919,23952,23953],{},"1,540",[1172,23955,23956],{"encoding":1174},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[1818,23959,23961],{"id":23960},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,23963,23964,23965,2529],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[1434,23966,23967],{},"I(1\u002Fx)",[3261,23969,23971],{"className":3263,"code":23970,"language":71,"meta":3265,"style":3265},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[1434,23972,23973,24000],{"__ignoreMap":3265},[1115,23974,23975,23978,23980,23982,23984,23986,23988,23990,23992,23994,23996,23998],{"class":3270,"line":10},[1115,23976,23977],{"class":3280},"model_hyperbola",[1115,23979,3291],{"class":3273},[1115,23981,21961],{"class":3294},[1115,23983,1151],{"class":3277},[1115,23985,21916],{"class":3280},[1115,23987,21968],{"class":3273},[1115,23989,23624],{"class":3294},[1115,23991,1151],{"class":3277},[1115,23993,1921],{"class":3312},[1115,23995,6292],{"class":3273},[1115,23997,21971],{"class":3280},[1115,23999,6019],{"class":3277},[1115,24001,24002,24004,24006,24008],{"class":3270,"line":27},[1115,24003,4267],{"class":3294},[1115,24005,1151],{"class":3277},[1115,24007,23977],{"class":3280},[1115,24009,3283],{"class":3277},[3261,24011,24014],{"className":24012,"code":24013,"language":4279,"meta":3265},[4277],"Call:\nlm(formula = tydenni_vydaje ~ I(1\u002Fpocet_clenu))\n\nResiduals:\n     1      2      3      4      5      6 \n 229.3 -400.7 -310.7 -130.7  153.3  459.3 \n\nCoefficients:\n                 Estimate Std. Error t value Pr(>|t|)   \n(Intercept)        2180.7      266.5   8.182  0.00122 **\nI(1\u002Fpocet_clenu)  -1920.0      534.6  -3.592  0.02293 * \n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 374.6 on 4 degrees of freedom\nMultiple R-squared:  0.7633,    Adjusted R-squared:  0.7041 \nF-statistic:  12.9 on 1 and 4 DF,  p-value: 0.02293\n",[1434,24015,24013],{"__ignoreMap":3265},[1110,24017,24018,24019,24053,24054,24075],{},"Model ",[1115,24020,24022],{"className":24021},[1136],[1138,24023,24024],{"xmlns":1140},[1142,24025,24026,24050],{},[1145,24027,24028,24034,24036,24039,24041],{},[1153,24029,24030,24032],{"accent":1121},[1156,24031,12274],{},[1148,24033,6165],{},[1148,24035,1914],{},[1919,24037,24038],{},"2180,7",[1148,24040,1990],{},[4995,24042,24043],{"scriptlevel":2780,"displaystyle":1121},[1916,24044,24045,24048],{},[1919,24046,24047],{},"1920,0",[1156,24049,1158],{},[1172,24051,24052],{"encoding":1174},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,24055,24057],{"className":24056},[1136],[1138,24058,24059],{"xmlns":1140},[1142,24060,24061,24073],{},[1145,24062,24063,24069,24071],{},[5465,24064,24065,24067],{},[1156,24066,1167],{},[1919,24068,2302],{},[1148,24070,1914],{},[1919,24072,22115],{},[1172,24074,22118],{"encoding":1174},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,24077,24079,24086,24117,24165],{"className":24078,"dataCallout":2145},[1106,2144],[1110,24080,24082,24085],{"className":24081},[1113],[1115,24083],{"className":24084,"ariaHidden":1121},[1118,2152,1120],"Příklad: Parabolická regrese",[1110,24087,24088,24089,24102,24103,24116],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,24090,24092],{"className":24091},[1136],[1138,24093,24094],{"xmlns":1140},[1142,24095,24096,24100],{},[1145,24097,24098],{},[1156,24099,1158],{},[1172,24101,1158],{"encoding":1174},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,24104,24106],{"className":24105},[1136],[1138,24107,24108],{"xmlns":1140},[1142,24109,24110,24114],{},[1145,24111,24112],{},[1156,24113,12274],{},[1172,24115,12274],{"encoding":1174},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,24118,22775,24119,1247],{},[1115,24120,24122],{"className":24121},[1136],[1138,24123,24124],{"xmlns":1140},[1142,24125,24126,24162],{},[1145,24127,24128,24134,24136,24138,24141,24143,24146,24148,24150,24152,24154,24156],{},[1153,24129,24130,24132],{"accent":1121},[1156,24131,12274],{},[1148,24133,6165],{},[1148,24135,1914],{},[1148,24137,1990],{},[1919,24139,24140],{},"60,3",[1148,24142,5066],{},[1919,24144,24145],{},"4,55",[5009,24147,5011],{},[1156,24149,1158],{},[1148,24151,1990],{},[1919,24153,9160],{},[5009,24155,5011],{},[5465,24157,24158,24160],{},[1156,24159,1158],{},[1919,24161,2302],{},[1172,24163,24164],{"encoding":1174},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,24166,24167,24168,24186],{},"Záporný koeficient ",[1115,24169,24171],{"className":24170},[1136],[1138,24172,24173],{"xmlns":1140},[1142,24174,24175,24183],{},[1145,24176,24177],{},[1217,24178,24179,24181],{},[1156,24180,16632],{},[1919,24182,2302],{},[1172,24184,24185],{"encoding":1174},"b_2"," znamená, že tržba s počtem zákazníků neroste neomezeně — funkce má maximum. Derivací a položením rovné nule vychází maximum přibližně při 45 zákaznících: nad tímto počtem zřejmě prodejna další zákazníky obsloužit nestíhá.",[1103,24188,24190,24197,24227,24272],{"className":24189,"dataCallout":2145},[1106,2144],[1110,24191,24193,24196],{"className":24192},[1113],[1115,24194],{"className":24195,"ariaHidden":1121},[1118,2152,1120],"Příklad: Hyperbolická regrese",[1110,24198,24199,24200,24213,24214,21205],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,24201,24203],{"className":24202},[1136],[1138,24204,24205],{"xmlns":1140},[1142,24206,24207,24211],{},[1145,24208,24209],{},[1156,24210,12274],{},[1172,24212,12274],{"encoding":1174},") na objemu produkce v tisících kusů (proměnná ",[1115,24215,24217],{"className":24216},[1136],[1138,24218,24219],{"xmlns":1140},[1142,24220,24221,24225],{},[1145,24222,24223],{},[1156,24224,1158],{},[1172,24226,1158],{"encoding":1174},[1110,24228,22775,24229,1247],{},[1115,24230,24232],{"className":24231},[1136],[1138,24233,24234],{"xmlns":1140},[1142,24235,24236,24269],{},[1145,24237,24238,24244,24246,24248,24251,24253],{},[1153,24239,24240,24242],{"accent":1121},[1156,24241,12274],{},[1148,24243,6165],{},[1148,24245,1914],{},[1148,24247,1990],{},[1919,24249,24250],{},"96,78",[1148,24252,5066],{},[4995,24254,24255],{"scriptlevel":2780,"displaystyle":1121},[1916,24256,24257,24267],{},[1145,24258,24259,24262,24264],{},[1919,24260,24261],{},"250",[5009,24263,5011],{},[1919,24265,24266],{},"528,88",[1156,24268,1158],{},[1172,24270,24271],{"encoding":1174},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,24273,24274,24275,24292],{},"Záporná hodnota ",[1115,24276,24278],{"className":24277},[1136],[1138,24279,24280],{"xmlns":1140},[1142,24281,24282,24290],{},[1145,24283,24284],{},[1217,24285,24286,24288],{},[1156,24287,16632],{},[1919,24289,1921],{},[1172,24291,21827],{"encoding":1174}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1437,24294,24296],{"id":24295},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,24298,24299,24300,2529],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1445,24301,21118],{},[1115,24303,24305],{"className":24304},[1136],[1138,24306,24307],{"xmlns":1140,"display":1897},[1142,24308,24309,24377],{},[1145,24310,24311,24317,24319,24341,24343,24345,24347,24375],{},[5465,24312,24313,24315],{},[1156,24314,1167],{},[1919,24316,2302],{},[1148,24318,1914],{},[1916,24320,24321,24333],{},[8555,24322,24323,24325,24331],{},[1156,24324,1198],{},[1153,24326,24327,24329],{"accent":1121},[1156,24328,12274],{},[1148,24330,6165],{},[1919,24332,2302],{},[8555,24334,24335,24337,24339],{},[1156,24336,1198],{},[1156,24338,12274],{},[1919,24340,2302],{},[1148,24342,1914],{},[1919,24344,1921],{},[1148,24346,1990],{},[1916,24348,24349,24367],{},[8555,24350,24351,24353,24365],{},[1156,24352,1198],{},[1145,24354,24355,24357,24359],{},[1156,24356,12274],{},[1148,24358,1990],{},[1153,24360,24361,24363],{"accent":1121},[1156,24362,12274],{},[1148,24364,6165],{},[1919,24366,2302],{},[8555,24368,24369,24371,24373],{},[1156,24370,1198],{},[1156,24372,12274],{},[1919,24374,2302],{},[1156,24376,1247],{"mathvariant":2014},[1172,24378,24379],{"encoding":1174},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,24381,24382,24383,24400,24401,24414],{},"Čím blíž je ",[1115,24384,24386],{"className":24385},[1136],[1138,24387,24388],{"xmlns":1140},[1142,24389,24390,24398],{},[1145,24391,24392],{},[5465,24393,24394,24396],{},[1156,24395,1167],{},[1919,24397,2302],{},[1172,24399,21136],{"encoding":1174}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,24402,24404],{"className":24403},[1136],[1138,24405,24406],{"xmlns":1140},[1142,24407,24408,24412],{},[1145,24409,24410],{},[1156,24411,12274],{},[1172,24413,12274],{"encoding":1174}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,24416,24417,24418,6884,24420,24443,24444,2529],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1445,24419,21140],{},[1115,24421,24423],{"className":24422},[1136],[1138,24424,24425],{"xmlns":1140},[1142,24426,24427,24441],{},[1145,24428,24429,24431,24433],{},[1156,24430,16330],{},[1148,24432,1914],{},[5460,24434,24435],{},[5465,24436,24437,24439],{},[1156,24438,1167],{},[1919,24440,2302],{},[1172,24442,21164],{"encoding":1174},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1445,24445,21168],{},[1115,24447,24449],{"className":24448},[1136],[1138,24450,24451],{"xmlns":1140,"display":1897},[1142,24452,24453,24503],{},[1145,24454,24455,24465,24467,24501],{},[1217,24456,24457,24459],{},[1156,24458,71],{},[1145,24460,24461,24463],{},[1156,24462,1158],{},[1156,24464,12274],{},[1148,24466,1914],{},[1916,24468,24469,24479],{},[1217,24470,24471,24473],{},[1156,24472,1198],{},[1145,24474,24475,24477],{},[1156,24476,1158],{},[1156,24478,12274],{},[5460,24480,24481],{},[1145,24482,24483,24491,24493],{},[8555,24484,24485,24487,24489],{},[1156,24486,1198],{},[1156,24488,1158],{},[1919,24490,2302],{},[1148,24492,13255],{},[8555,24494,24495,24497,24499],{},[1156,24496,1198],{},[1156,24498,12274],{},[1919,24500,2302],{},[1156,24502,1247],{"mathvariant":2014},[1172,24504,24505],{"encoding":1174},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,24507,24508,24509,24525,24526,24542],{},"Koeficient korelace nabývá hodnot od ",[1115,24510,24512],{"className":24511},[1136],[1138,24513,24514],{"xmlns":1140},[1142,24515,24516,24522],{},[1145,24517,24518,24520],{},[1148,24519,1990],{},[1919,24521,1921],{},[1172,24523,24524],{"encoding":1174},"-1"," do ",[1115,24527,24529],{"className":24528},[1136],[1138,24530,24531],{"xmlns":1140},[1142,24532,24533,24539],{},[1145,24534,24535,24537],{},[1148,24536,5066],{},[1919,24538,1921],{},[1172,24540,24541],{"encoding":1174},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,24544,24545],{},[1527,24546],{"alt":24547,"className":24548,"src":24549},"mask-ra-korelace-sila",[1531,1532],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,24551,24552,24553,24566,24567,24585,24586,1204,24599,24612],{},"S rostoucí absolutní hodnotou ",[1115,24554,24556],{"className":24555},[1136],[1138,24557,24558],{"xmlns":1140},[1142,24559,24560,24564],{},[1145,24561,24562],{},[1156,24563,71],{},[1172,24565,71],{"encoding":1174}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,24568,24570],{"className":24569},[1136],[1138,24571,24572],{"xmlns":1140},[1142,24573,24574,24582],{},[1145,24575,24576,24578,24580],{},[1156,24577,71],{},[1148,24579,14579],{},[1919,24581,2780],{},[1172,24583,24584],{"encoding":1174},"r\\approx 0"," je mezi ",[1115,24587,24589],{"className":24588},[1136],[1138,24590,24591],{"xmlns":1140},[1142,24592,24593,24597],{},[1145,24594,24595],{},[1156,24596,1158],{},[1172,24598,1158],{"encoding":1174},[1115,24600,24602],{"className":24601},[1136],[1138,24603,24604],{"xmlns":1140},[1142,24605,24606,24610],{},[1145,24607,24608],{},[1156,24609,12274],{},[1172,24611,12274],{"encoding":1174}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[1818,24614,21860],{"id":24615},"v-r-1",[3261,24617,24619],{"className":3263,"code":24618,"language":71,"meta":3265,"style":3265},"cor(pocet_clenu, tydenni_vydaje)\n",[1434,24620,24621],{"__ignoreMap":3265},[1115,24622,24623,24626,24628,24630,24632,24635],{"class":3270,"line":10},[1115,24624,24625],{"class":3294},"cor",[1115,24627,1151],{"class":3277},[1115,24629,21881],{"class":3280},[1115,24631,1164],{"class":3273},[1115,24633,24634],{"class":3280}," tydenni_vydaje",[1115,24636,3283],{"class":3277},[3261,24638,24641],{"className":24639,"code":24640,"language":4279,"meta":3265},[4277],"[1] 0.9997441\n",[1434,24642,24640],{"__ignoreMap":3265},[1110,24644,24645,24646,24672],{},"Hodnota 0,9997 odpovídá ",[1115,24647,24649],{"className":24648},[1136],[1138,24650,24651],{"xmlns":1140},[1142,24652,24653,24669],{},[1145,24654,24655,24663,24665],{},[5460,24656,24657],{},[5465,24658,24659,24661],{},[1156,24660,1167],{},[1919,24662,2302],{},[1148,24664,1914],{},[5460,24666,24667],{},[1919,24668,22115],{},[1172,24670,24671],{"encoding":1174},"\\sqrt{R^2}=\\sqrt{0{,}9995}"," ze summary regresní přímky výše — přesně tak, jak definice říká: pro přímkovou regresi je koeficient korelace roven indexu korelace.",[1103,24674,24676,24683,24686],{"className":24675,"dataCallout":2145},[1106,2144],[1110,24677,24679,24682],{"className":24678},[1113],[1115,24680],{"className":24681,"ariaHidden":1121},[1118,2152,1120],"Příklad: Koeficient korelace",[1110,24684,24685],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,24687,22775,24688,24715],{},[1115,24689,24691],{"className":24690},[1136],[1138,24692,24693],{"xmlns":1140},[1142,24694,24695,24712],{},[1145,24696,24697,24707,24709],{},[1217,24698,24699,24701],{},[1156,24700,71],{},[1145,24702,24703,24705],{},[1156,24704,1158],{},[1156,24706,12274],{},[1148,24708,1914],{},[1919,24710,24711],{},"0,739",[1172,24713,24714],{"encoding":1174},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1437,24717,24719],{"id":24718},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,24721,24722,24723,24736],{},"Pokud na závisle proměnnou ",[1115,24724,24726],{"className":24725},[1136],[1138,24727,24728],{"xmlns":1140},[1142,24729,24730,24734],{},[1145,24731,24732],{},[1156,24733,12274],{},[1172,24735,12274],{"encoding":1174}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,24738,24740],{"className":24739},[1136],[1138,24741,24742],{"xmlns":1140,"display":1897},[1142,24743,24744,24854],{},[1145,24745,24746,24748,24750,24756,24758,24764,24770,24772,24778,24784,24786,24788,24790,24796,24802,24804,24806,24812,24814,24820,24822,24828,24834,24836,24838,24840,24846,24852],{},[1156,24747,21434],{},[1148,24749,1914],{},[1217,24751,24752,24754],{},[1156,24753,21449],{},[1919,24755,2780],{},[1148,24757,5066],{},[1217,24759,24760,24762],{},[1156,24761,21449],{},[1919,24763,1921],{},[1217,24765,24766,24768],{},[1156,24767,1158],{},[1919,24769,1921],{},[1148,24771,5066],{},[1217,24773,24774,24776],{},[1156,24775,21449],{},[1919,24777,2302],{},[1217,24779,24780,24782],{},[1156,24781,1158],{},[1919,24783,2302],{},[1148,24785,5066],{},[1148,24787,23025],{},[1148,24789,5066],{},[1217,24791,24792,24794],{},[1156,24793,21449],{},[1156,24795,1110],{},[1217,24797,24798,24800],{},[1156,24799,1158],{},[1156,24801,1110],{},[1148,24803,1164],{"separator":1121},[1954,24805],{"width":1956},[1153,24807,24808,24810],{"accent":1121},[1156,24809,12274],{},[1148,24811,6165],{},[1148,24813,1914],{},[1217,24815,24816,24818],{},[1156,24817,16632],{},[1919,24819,2780],{},[1148,24821,5066],{},[1217,24823,24824,24826],{},[1156,24825,16632],{},[1919,24827,1921],{},[1217,24829,24830,24832],{},[1156,24831,1158],{},[1919,24833,1921],{},[1148,24835,5066],{},[1148,24837,23025],{},[1148,24839,5066],{},[1217,24841,24842,24844],{},[1156,24843,16632],{},[1156,24845,1110],{},[1217,24847,24848,24850],{},[1156,24849,1158],{},[1156,24851,1110],{},[1156,24853,1247],{"mathvariant":2014},[1172,24855,24856],{"encoding":1174},"\\eta = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + \\dots + \\beta_p x_p, \\qquad \\hat y = b_0 + b_1 x_1 + \\dots + b_p x_p.",[1818,24858,24860],{"id":24859},"výběr-proměnných","Výběr proměnných",[1124,24862,24863,24869],{},[1127,24864,24865,24868],{},[1445,24866,24867],{},"Metoda ENTER"," — vloží do modelu všechny proměnné najednou. Použije se, když jde o index determinace celého modelu, o vliv každé nezávislé proměnné při kontrole vlivu ostatních, nebo o relativní důležitost proměnných. Vyžaduje poměrně vysoký počet pozorování — aspoň 20 na každou proměnnou.",[1127,24870,24871,24874,24875,24878,24879,24882],{},[1445,24872,24873],{},"Metoda stepwise (postupná regrese)"," — hledá „nejlepší\" model (co nejmíň proměnných, co nejkvalitnější predikce) na základě F-testu; pořadí vstupu\u002Fodebrání proměnných řídí program, ne uživatel. Varianta ",[1445,24876,24877],{},"forward"," proměnné postupně přidává, varianta ",[1445,24880,24881],{},"backward"," naopak začíná plným modelem a proměnné postupně odebírá. Pořadí vkládání ovlivňuje odhad důležitosti proměnných, proto je třeba metodu zvolit uvážlivě. Stepwise vyžaduje ještě víc pozorování — aspoň 40 na proměnnou.",[1818,24884,24886],{"id":24885},"postup-odhadu","Postup odhadu",[1538,24888,24889,24892,24895],{},[1127,24890,24891],{},"ověření předpokladů regresního modelu,",[1127,24893,24894],{},"samotný odhad parametrů,",[1127,24896,24897],{},"reziduální analýza výsledného modelu.",[1110,24899,24900,24901,24918,24919,4984,24921,24950,24951,24980,24981,24998],{},"Důležitost každého parametru ",[1115,24902,24904],{"className":24903},[1136],[1138,24905,24906],{"xmlns":1140},[1142,24907,24908,24916],{},[1145,24909,24910],{},[1217,24911,24912,24914],{},[1156,24913,16632],{},[1156,24915,1223],{},[1172,24917,21574],{"encoding":1174}," v modelu ověřuje ",[1445,24920,992],{},[1115,24922,24924],{"className":24923},[1136],[1138,24925,24926],{"xmlns":1140},[1142,24927,24928,24948],{},[1145,24929,24930,24936,24938,24944,24946],{},[1217,24931,24932,24934],{},[1156,24933,6797],{},[1919,24935,2780],{},[1148,24937,2529],{},[1217,24939,24940,24942],{},[1156,24941,21449],{},[1156,24943,1223],{},[1148,24945,1914],{},[1919,24947,2780],{},[1172,24949,22059],{"encoding":1174}," (proměnná je v modelu nevýznamná) proti ",[1115,24952,24954],{"className":24953},[1136],[1138,24955,24956],{"xmlns":1140},[1142,24957,24958,24978],{},[1145,24959,24960,24966,24968,24974,24976],{},[1217,24961,24962,24964],{},[1156,24963,6797],{},[1919,24965,1921],{},[1148,24967,2529],{},[1217,24969,24970,24972],{},[1156,24971,21449],{},[1156,24973,1223],{},[1148,24975,16087],{"mathvariant":2014},[1919,24977,2780],{},[1172,24979,22090],{"encoding":1174}," (proměnná je významná). Při nezamítnutí ",[1115,24982,24984],{"className":24983},[1136],[1138,24985,24986],{"xmlns":1140},[1142,24987,24988,24996],{},[1145,24989,24990],{},[1217,24991,24992,24994],{},[1156,24993,6797],{},[1919,24995,2780],{},[1172,24997,6802],{"encoding":1174}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[1818,25000,25002],{"id":25001},"předpoklady-modelu","Předpoklady modelu",[1538,25004,25005,25022,25055,25061,25064,25067],{},[1127,25006,25007,25008,25021],{},"Závisle proměnná ",[1115,25009,25011],{"className":25010},[1136],[1138,25012,25013],{"xmlns":1140},[1142,25014,25015,25019],{},[1145,25016,25017],{},[1156,25018,12274],{},[1172,25020,12274],{"encoding":1174}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1127,25023,25024,25025,25054],{},"Nezávislé proměnné ",[1115,25026,25028],{"className":25027},[1136],[1138,25029,25030],{"xmlns":1140},[1142,25031,25032,25052],{},[1145,25033,25034,25040,25042,25044,25046],{},[1217,25035,25036,25038],{},[1156,25037,1158],{},[1919,25039,1921],{},[1148,25041,1164],{"separator":1121},[1148,25043,2043],{},[1148,25045,1164],{"separator":1121},[1217,25047,25048,25050],{},[1156,25049,1158],{},[1156,25051,1110],{},[1172,25053,21398],{"encoding":1174}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1127,25056,25057,25058,1247],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1445,25059,25060],{},"multikolinearita",[1127,25062,25063],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1127,25065,25066],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1127,25068,25069,25070,25074],{},"Proměnné mají mít ",[6613,25071,25073],{"className":25072,"dataFsResolvedFilePath":6631,"href":6632},[1531],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,25076,25077,25078,25081],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[6613,25079,6949],{"className":25080,"dataFsResolvedFilePath":6639,"href":6640},[1531],") — Shapiro–Wilkovým nebo Kolmogorovovým–Smirnovovým testem — nebo graficky grafem reziduí proti predikovaným hodnotám, kde by body měly být rovnoměrně rozptýlené po obou stranách vodorovné osy.",[1818,25083,25084],{"id":25060},"Multikolinearita",[1110,25086,25087],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1124,25089,25090,25093,25096],{},[1127,25091,25092],{},"výsledky regrese jsou pak nespolehlivé,",[1127,25094,25095],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1127,25097,25098],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,25100,25101,25102,25105,25106,25129,25130,25148,25149,25165],{},"Pozná se podle vysokých korelačních koeficientů mezi regresory (nad 0,75), podle toho, že celkový F-test modelu je významný, ale jednotlivé t-testy parametrů ne, nebo softwarově přes ",[1445,25103,25104],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,25107,25109],{"className":25108},[1136],[1138,25110,25111],{"xmlns":1140},[1142,25112,25113,25126],{},[1145,25114,25115,25117,25119,25122,25124],{},[1919,25116,1921],{},[1148,25118,5682],{},[5009,25120,25121],{},"VIF",[1148,25123,5682],{},[1919,25125,2424],{},[1172,25127,25128],{"encoding":1174},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,25131,25133],{"className":25132},[1136],[1138,25134,25135],{"xmlns":1140},[1142,25136,25137,25145],{},[1145,25138,25139,25141,25143],{},[5009,25140,25121],{},[1148,25142,5755],{},[1919,25144,2424],{},[1172,25146,25147],{"encoding":1174},"\\text{VIF}>5"," (přísněji ",[1115,25150,25152],{"className":25151},[1136],[1138,25153,25154],{"xmlns":1140},[1142,25155,25156,25162],{},[1145,25157,25158,25160],{},[1148,25159,5755],{},[1919,25161,14175],{},[1172,25163,25164],{"encoding":1174},">10",") značí vysokou multikolinearitu.",[1110,25167,25168],{},"Řešení: je-li multikolinearita způsobená silnou závislostí dvou proměnných, jednu z nich se z modelu vyřadí; je-li způsobená závislostí víc proměnných najednou, použije se metoda hlavních komponent a pracuje se s novými, nekorelovanými proměnnými.",[1818,25170,25172],{"id":25171},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1124,25174,25175,25181,25187],{},[1127,25176,25177,25180],{},[1445,25178,25179],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1127,25182,25183,25186],{},[1445,25184,25185],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1127,25188,25189,25192,25193,25196],{},[1445,25190,25191],{},"AIC"," (Akaikeho informační kritérium) a ",[1445,25194,25195],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[1818,25198,21860],{"id":25199},"v-r-2",[1110,25201,25202],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3261,25204,25206],{"className":3263,"code":25205,"language":71,"meta":3265,"style":3265},"data \u003C- read.table(\"4_4.txt\", header = TRUE)\nmodel_plny \u003C- lm(y ~ x1 + x2 + x3 + x4, data = data)\nmodel_krok \u003C- step(model_plny, direction = \"both\")\nsummary(model_krok)\n\nlibrary(car)\nvif(model_krok)\n\nlibrary(lmtest)\ndwtest(model_krok)\n\nlibrary(whitestrap)\nwhite_test(model_krok)\n\nshapiro.test(residuals(model_krok))\n",[1434,25207,25208,25231,25274,25300,25310,25314,25325,25336,25340,25350,25360,25364,25374,25384,25389],{"__ignoreMap":3265},[1115,25209,25210,25212,25214,25216,25218,25221,25223,25225,25227,25229],{"class":3270,"line":10},[1115,25211,3288],{"class":3280},[1115,25213,3291],{"class":3273},[1115,25215,3295],{"class":3294},[1115,25217,1151],{"class":3277},[1115,25219,25220],{"class":3300},"\"4_4.txt\"",[1115,25222,1164],{"class":3273},[1115,25224,3306],{"class":3280},[1115,25226,3309],{"class":3273},[1115,25228,3313],{"class":3312},[1115,25230,3283],{"class":3277},[1115,25232,25233,25236,25238,25240,25242,25244,25246,25249,25251,25254,25256,25259,25261,25264,25266,25268,25270,25272],{"class":3270,"line":27},[1115,25234,25235],{"class":3280},"model_plny",[1115,25237,3291],{"class":3273},[1115,25239,21961],{"class":3294},[1115,25241,1151],{"class":3277},[1115,25243,12274],{"class":3280},[1115,25245,21968],{"class":3273},[1115,25247,25248],{"class":3280}," x1",[1115,25250,6170],{"class":3273},[1115,25252,25253],{"class":3280}," x2",[1115,25255,6170],{"class":3273},[1115,25257,25258],{"class":3280}," x3",[1115,25260,6170],{"class":3273},[1115,25262,25263],{"class":3280}," x4",[1115,25265,1164],{"class":3273},[1115,25267,4514],{"class":3280},[1115,25269,3309],{"class":3273},[1115,25271,4514],{"class":3280},[1115,25273,3283],{"class":3277},[1115,25275,25276,25279,25281,25284,25286,25288,25290,25293,25295,25298],{"class":3270,"line":148},[1115,25277,25278],{"class":3280},"model_krok",[1115,25280,3291],{"class":3273},[1115,25282,25283],{"class":3294}," step",[1115,25285,1151],{"class":3277},[1115,25287,25235],{"class":3280},[1115,25289,1164],{"class":3273},[1115,25291,25292],{"class":3280}," direction",[1115,25294,3309],{"class":3273},[1115,25296,25297],{"class":3300}," \"both\"",[1115,25299,3283],{"class":3277},[1115,25301,25302,25304,25306,25308],{"class":3270,"line":111},[1115,25303,4267],{"class":3294},[1115,25305,1151],{"class":3277},[1115,25307,25278],{"class":3280},[1115,25309,3283],{"class":3277},[1115,25311,25312],{"class":3270,"line":96},[1115,25313,4237],{"emptyLinePlaceholder":4236},[1115,25315,25316,25318,25320,25323],{"class":3270,"line":89},[1115,25317,3274],{"class":3273},[1115,25319,1151],{"class":3277},[1115,25321,25322],{"class":3280},"car",[1115,25324,3283],{"class":3277},[1115,25326,25327,25330,25332,25334],{"class":3270,"line":82},[1115,25328,25329],{"class":3294},"vif",[1115,25331,1151],{"class":3277},[1115,25333,25278],{"class":3280},[1115,25335,3283],{"class":3277},[1115,25337,25338],{"class":3270,"line":75},[1115,25339,4237],{"emptyLinePlaceholder":4236},[1115,25341,25342,25344,25346,25348],{"class":3270,"line":9071},[1115,25343,3274],{"class":3273},[1115,25345,1151],{"class":3277},[1115,25347,22509],{"class":3280},[1115,25349,3283],{"class":3277},[1115,25351,25352,25354,25356,25358],{"class":3270,"line":72},[1115,25353,22516],{"class":3294},[1115,25355,1151],{"class":3277},[1115,25357,25278],{"class":3280},[1115,25359,3283],{"class":3277},[1115,25361,25362],{"class":3270,"line":25},[1115,25363,4237],{"emptyLinePlaceholder":4236},[1115,25365,25366,25368,25370,25372],{"class":3270,"line":65},[1115,25367,3274],{"class":3273},[1115,25369,1151],{"class":3277},[1115,25371,22599],{"class":3280},[1115,25373,3283],{"class":3277},[1115,25375,25376,25378,25380,25382],{"class":3270,"line":63},[1115,25377,22606],{"class":3294},[1115,25379,1151],{"class":3277},[1115,25381,25278],{"class":3280},[1115,25383,3283],{"class":3277},[1115,25385,25387],{"class":3270,"line":25386},14,[1115,25388,4237],{"emptyLinePlaceholder":4236},[1115,25390,25391,25393,25395,25397,25399,25401],{"class":3270,"line":60},[1115,25392,22684],{"class":3294},[1115,25394,1151],{"class":3277},[1115,25396,22154],{"class":3294},[1115,25398,1151],{"class":3277},[1115,25400,25278],{"class":3280},[1115,25402,6019],{"class":3277},[1110,25404,25405,25407,25408,25411],{},[1434,25406,21232],{}," provádí stepwise výběr podle AIC, ",[1434,25409,25410],{},"vif()"," spočítá Variance Inflation Factor pro každý regresor v modelu, zbylé tři volání ověřují stejné tři předpoklady (autokorelace, homoskedasticita, normalita reziduí) jako u regresní přímky výše.",[1103,25413,25415,25422,25425,25428],{"className":25414,"dataCallout":2145},[1106,2144],[1110,25416,25418,25421],{"className":25417},[1113],[1115,25419],{"className":25420,"ariaHidden":1121},[1118,2152,1120],"Příklad: Vícenásobná regrese",[1110,25423,25424],{},"U souboru nemovitostí prodaných v roce 1981 se sledovala prodejní cena v dolarech v závislosti na stáří nemovitosti, počtu sousedících nemovitostí, velikosti podlahové plochy a pozemku, vzdálenosti k mezistátní silnici, vzdálenosti ke spalovně a počtu pokojů a koupelen. Úkolem bylo odhadnout model, který by dobře popisoval data.",[1110,25426,25427],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,25429,25430,25431,25434,25435,25437,25438,25441],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1445,25432,25433],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1445,25436,25060],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1445,25439,25440],{},"odlehlá pozorování"," — vhodné je provést ještě test a případně je vyřadit. Výsledný model obsahoval i nevýznamné proměnné, jako celek však byl statisticky významný s přibližně průměrným indexem determinace; dalšího zlepšení šlo dosáhnout snížením AIC pomocí stepwise regrese.",[1437,25443,6378],{"id":6377},[1103,25445,25447,25454],{"className":25446,"dataCallout":11568},[1106,11567],[1110,25448,25450,25453],{"className":25449},[1113],[1115,25451],{"className":25452,"ariaHidden":1121},[1118,11575,1120],"Koeficient korelace jen pro přímku",[1110,25455,25456,25457,25513,25514,25531,25532,25552,25553,1204,25566,1247],{},"Vzorec ",[1115,25458,25460],{"className":25459},[1136],[1138,25461,25462],{"xmlns":1140},[1142,25463,25464,25510],{},[1145,25465,25466,25476,25478,25488,25490],{},[1217,25467,25468,25470],{},[1156,25469,71],{},[1145,25471,25472,25474],{},[1156,25473,1158],{},[1156,25475,12274],{},[1148,25477,1914],{},[1217,25479,25480,25482],{},[1156,25481,1198],{},[1145,25483,25484,25486],{},[1156,25485,1158],{},[1156,25487,12274],{},[1156,25489,4412],{"mathvariant":2014},[5460,25491,25492],{},[1145,25493,25494,25502],{},[8555,25495,25496,25498,25500],{},[1156,25497,1198],{},[1156,25499,1158],{},[1919,25501,2302],{},[8555,25503,25504,25506,25508],{},[1156,25505,1198],{},[1156,25507,12274],{},[1919,25509,2302],{},[1172,25511,25512],{"encoding":1174},"r_{xy}=s_{xy}\u002F\\sqrt{s_x^2 s_y^2}"," měří lineární závislost. Pro nelineární regresní funkci (parabola, hyperbola, exponenciála) se kvalita fitu posuzuje indexem determinace ",[1115,25515,25517],{"className":25516},[1136],[1138,25518,25519],{"xmlns":1140},[1142,25520,25521,25529],{},[1145,25522,25523],{},[5465,25524,25525,25527],{},[1156,25526,1167],{},[1919,25528,2302],{},[1172,25530,21136],{"encoding":1174},", případně obecným indexem korelace ",[1115,25533,25535],{"className":25534},[1136],[1138,25536,25537],{"xmlns":1140},[1142,25538,25539,25549],{},[1145,25540,25541],{},[5460,25542,25543],{},[5465,25544,25545,25547],{},[1156,25546,1167],{},[1919,25548,2302],{},[1172,25550,25551],{"encoding":1174},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,25554,25556],{"className":25555},[1136],[1138,25557,25558],{"xmlns":1140},[1142,25559,25560,25564],{},[1145,25561,25562],{},[1156,25563,1158],{},[1172,25565,1158],{"encoding":1174},[1115,25567,25569],{"className":25568},[1136],[1138,25570,25571],{"xmlns":1140},[1142,25572,25573,25577],{},[1145,25574,25575],{},[1156,25576,12274],{},[1172,25578,12274],{"encoding":1174},[1103,25580,25582,25589],{"className":25581,"dataCallout":11568},[1106,11567],[1110,25583,25585,25588],{"className":25584},[1113],[1115,25586],{"className":25587,"ariaHidden":1121},[1118,11575,1120],"Významný F-test, nevýznamné t-testy",[1110,25590,25591],{},"Pokud je celkový F-test modelu významný, ale jednotlivé t-testy parametrů ne, nejde nutně o chybně zvolené proměnné — je to typický příznak multikolinearity. Řešením je zkontrolovat VIF, ne mechanicky vyřazovat „nevýznamné\" proměnné.",[1103,25593,25595,25602],{"className":25594,"dataCallout":11568},[1106,11567],[1110,25596,25598,25601],{"className":25597},[1113],[1115,25599],{"className":25600,"ariaHidden":1121},[1118,11575,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,25603,25604],{},"DW se pohybuje od 0 do 4; hodnoty blízko 2 znamenají žádnou autokorelaci, blízko 0 pozitivní autokorelaci, blízko 4 negativní autokorelaci. Samotná odchylka od 2 bez pohledu na p-hodnotu testu nic neprokazuje — rozhoduje až test, ne vzdálenost od 2.",[1103,25606,25608,25615],{"className":25607,"dataCallout":11568},[1106,11567],[1110,25609,25611,25614],{"className":25610},[1113],[1115,25612],{"className":25613,"ariaHidden":1121},[1118,11575,1120],"Nízký počet pozorování při stepwise výběru",[1110,25616,25617],{},"Metoda ENTER potřebuje aspoň 20 pozorování na proměnnou, stepwise regrese aspoň 40. Při menším vzorku jsou výsledky výběru proměnných nespolehlivé bez ohledu na to, jak hezky vychází 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,"path":40515,"seo":40516,"sources":40517,"stem":40523,"tags":40524,"type":6748,"updated":6736,"__hash__":40525},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":30704,"toc":40487},[30705,30708,30907,30951,30955,30965,30968,31034,31084,31237,31241,31244,31338,31488,31507,31514,31603,31607,31642,31679,31717,31752,31756,31763,31981,32100,32104,32236,32290,32312,32654,32661,32749,32755,32796,33081,33090,33205,33211,33218,33223,33229,33323,33329,33355,33361,33453,33459,33509,33513,33709,33769,34131,34470,34569,34575,34803,34807,35073,35077,35080,35146,35193,35649,35653,35656,35843,35876,36098,36417,36456,36463,37120,37259,37265,37421,37427,37434,37487,37493,37666,37672,37736,37741,37926,37932,37977,37981,37984,37988,38035,38263,38279,38368,38374,38400,38404,38407,38479,38572,38641,38647,38670,39117,39124,39128,39158,39162,39412,39431,39492,39501,39657,39663,39689,39864,39868,39889,39920,39924,39948,39978,39982,40042,40100,40104,40111,40284,40286,40439,40441,40478,40480,40484],[1099,30706,11762],{"id":30707},"testování-statistických-hypotéz",[1103,30709,30711,30717],{"className":30710,"dataCallout":1108},[1106,1107],[1110,30712,30714,1122],{"className":30713},[1113],[1115,30715],{"className":30716,"ariaHidden":1121},[1118,1119,1120],[1124,30718,30719,30789,30871,30874,30877],{},[1127,30720,30721,30722,30739,30740,30757,30758,1176,30771,30788],{},"Test porovnává tvrzení ",[1115,30723,30725],{"className":30724},[1136],[1138,30726,30727],{"xmlns":1140},[1142,30728,30729,30737],{},[1145,30730,30731],{},[1217,30732,30733,30735],{},[1156,30734,6797],{},[1919,30736,2780],{},[1172,30738,6802],{"encoding":1174}," s alternativou ",[1115,30741,30743],{"className":30742},[1136],[1138,30744,30745],{"xmlns":1140},[1142,30746,30747,30755],{},[1145,30748,30749],{},[1217,30750,30751,30753],{},[1156,30752,6797],{},[1919,30754,1921],{},[1172,30756,8200],{"encoding":1174}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,30759,30761],{"className":30760},[1136],[1138,30762,30763],{"xmlns":1140},[1142,30764,30765,30769],{},[1145,30766,30767],{},[1156,30768,6835],{},[1172,30770,6835],{"encoding":1174},[1115,30772,30774],{"className":30773},[1136],[1138,30775,30776],{"xmlns":1140},[1142,30777,30778,30786],{},[1145,30779,30780],{},[1217,30781,30782,30784],{},[1156,30783,6797],{},[1919,30785,2780],{},[1172,30787,6802],{"encoding":1174}," zamítáme.",[1127,30790,30791,30792,30805,30806,30823,30824,30838,30839,30856,30857,30870],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,30793,30795],{"className":30794},[1136],[1138,30796,30797],{"xmlns":1140},[1142,30798,30799,30803],{},[1145,30800,30801],{},[1156,30802,8567],{},[1172,30804,8630],{"encoding":1174},", zamítnutí platné ",[1115,30807,30809],{"className":30808},[1136],[1138,30810,30811],{"xmlns":1140},[1142,30812,30813,30821],{},[1145,30814,30815],{},[1217,30816,30817,30819],{},[1156,30818,6797],{},[1919,30820,2780],{},[1172,30822,6802],{"encoding":1174},") a chybu II. druhu (",[1115,30825,30827],{"className":30826},[1136],[1138,30828,30829],{"xmlns":1140},[1142,30830,30831,30835],{},[1145,30832,30833],{},[1156,30834,21449],{},[1172,30836,30837],{"encoding":1174},"\\beta",", přijetí neplatné ",[1115,30840,30842],{"className":30841},[1136],[1138,30843,30844],{"xmlns":1140},[1142,30845,30846,30854],{},[1145,30847,30848],{},[1217,30849,30850,30852],{},[1156,30851,6797],{},[1919,30853,2780],{},[1172,30855,6802],{"encoding":1174},"). Hladina významnosti ",[1115,30858,30860],{"className":30859},[1136],[1138,30861,30862],{"xmlns":1140},[1142,30863,30864,30868],{},[1145,30865,30866],{},[1156,30867,8567],{},[1172,30869,8630],{"encoding":1174}," se volí předem, obvykle 0,05.",[1127,30872,30873],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1127,30875,30876],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1127,30878,30879,30880,30893,30894,1247],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,30881,30883],{"className":30882},[1136],[1138,30884,30885],{"xmlns":1140},[1142,30886,30887,30891],{},[1145,30888,30889],{},[1156,30890,6835],{},[1172,30892,6835],{"encoding":1174},", nebo podle p-hodnoty vůči ",[1115,30895,30897],{"className":30896},[1136],[1138,30898,30899],{"xmlns":1140},[1142,30900,30901,30905],{},[1145,30902,30903],{},[1156,30904,8567],{},[1172,30906,8630],{"encoding":1174},[1110,30908,30909,30910,30914,30915,30919,30920,30924,30925,1176,30938,21205],{},"Testy statistických hypotéz jsou nástroj ",[6613,30911,30913],{"className":30912,"dataFsResolvedFilePath":6616,"href":6617},[1531],"Metod aplikované statistiky"," pro rozhodování o parametrech nebo tvaru rozdělení na základě náhodného výběru, nikoli vyčerpávajícího šetření celého základního souboru. Vycházejí z charakteristik, které lze předem spočítat jako ",[6613,30916,30918],{"className":30917,"dataFsResolvedFilePath":6624,"href":6625},[1531],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[6613,30921,30923],{"className":30922,"dataFsResolvedFilePath":6631,"href":6632},[1531],"náhodných veličin"," (normální, ",[1115,30926,30928],{"className":30927},[1136],[1138,30929,30930],{"xmlns":1140},[1142,30931,30932,30936],{},[1145,30933,30934],{},[1156,30935,12288],{},[1172,30937,12288],{"encoding":1174},[1115,30939,30941],{"className":30940},[1136],[1138,30942,30943],{"xmlns":1140},[1142,30944,30945,30949],{},[1145,30946,30947],{},[1156,30948,11867],{},[1172,30950,11867],{"encoding":1174},[1437,30952,30954],{"id":30953},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,30956,30957,30960,30961,30964],{},[1445,30958,30959],{},"Statistická hypotéza"," je předpoklad o parametru nebo tvaru rozdělení zkoumaného znaku — například že určitý typ auta má průměrnou spotřebu 7 l\u002F100 km. Ověřit ji na celém základním souboru je obvykle neekonomické nebo technicky neproveditelné, a tak se posuzuje na výběru. ",[1445,30962,30963],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,30966,30967],{},"Proti sobě stojí dvě hypotézy:",[1124,30969,30970,30993],{},[1127,30971,30972,30992],{},[1445,30973,30974,30975],{},"Nulová hypotéza ",[1115,30976,30978],{"className":30977},[1136],[1138,30979,30980],{"xmlns":1140},[1142,30981,30982,30990],{},[1145,30983,30984],{},[1217,30985,30986,30988],{},[1156,30987,6797],{},[1919,30989,2780],{},[1172,30991,6802],{"encoding":1174}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1127,30994,30995,31015,31016,31033],{},[1445,30996,30997,30998],{},"Alternativní hypotéza ",[1115,30999,31001],{"className":31000},[1136],[1138,31002,31003],{"xmlns":1140},[1142,31004,31005,31013],{},[1145,31006,31007],{},[1217,31008,31009,31011],{},[1156,31010,6797],{},[1919,31012,1921],{},[1172,31014,8200],{"encoding":1174}," — staví se proti ",[1115,31017,31019],{"className":31018},[1136],[1138,31020,31021],{"xmlns":1140},[1142,31022,31023,31031],{},[1145,31024,31025],{},[1217,31026,31027,31029],{},[1156,31028,6797],{},[1919,31030,2780],{},[1172,31032,6802],{"encoding":1174}," a určitým způsobem popírá její tvrzení.",[1110,31035,6926,31036,31066,31067,2529],{},[1115,31037,31039],{"className":31038},[1136],[1138,31040,31041],{"xmlns":1140},[1142,31042,31043,31063],{},[1145,31044,31045,31051,31053,31055,31057],{},[1217,31046,31047,31049],{},[1156,31048,6797],{},[1919,31050,2780],{},[1148,31052,2529],{},[1156,31054,1677],{},[1148,31056,1914],{},[1217,31058,31059,31061],{},[1156,31060,1677],{},[1919,31062,2780],{},[1172,31064,31065],{"encoding":1174},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,31068,31070],{"className":31069},[1136],[1138,31071,31072],{"xmlns":1140},[1142,31073,31074,31082],{},[1145,31075,31076],{},[1217,31077,31078,31080],{},[1156,31079,6797],{},[1919,31081,1921],{},[1172,31083,8200],{"encoding":1174},[1459,31085,31086,31116],{},[1462,31087,31088],{},[1465,31089,31090,31110,31113],{},[1468,31091,31092,31093],{},"Tvar ",[1115,31094,31096],{"className":31095},[1136],[1138,31097,31098],{"xmlns":1140},[1142,31099,31100,31108],{},[1145,31101,31102],{},[1217,31103,31104,31106],{},[1156,31105,6797],{},[1919,31107,1921],{},[1172,31109,8200],{"encoding":1174},[1468,31111,31112],{},"Zápis",[1468,31114,31115],{},"Typ",[1477,31117,31118,31158,31198],{},[1465,31119,31120,31123,31155],{},[1482,31121,31122],{},"nerovnost",[1482,31124,31125],{},[1115,31126,31128],{"className":31127},[1136],[1138,31129,31130],{"xmlns":1140},[1142,31131,31132,31152],{},[1145,31133,31134,31140,31142,31144,31146],{},[1217,31135,31136,31138],{},[1156,31137,6797],{},[1919,31139,1921],{},[1148,31141,2529],{},[1156,31143,1677],{},[1148,31145,16087],{"mathvariant":2014},[1217,31147,31148,31150],{},[1156,31149,1677],{},[1919,31151,2780],{},[1172,31153,31154],{"encoding":1174},"H_1: \\mu \\neq \\mu_0",[1482,31156,31157],{},"dvoustranná",[1465,31159,31160,31163,31195],{},[1482,31161,31162],{},"větší",[1482,31164,31165],{},[1115,31166,31168],{"className":31167},[1136],[1138,31169,31170],{"xmlns":1140},[1142,31171,31172,31192],{},[1145,31173,31174,31180,31182,31184,31186],{},[1217,31175,31176,31178],{},[1156,31177,6797],{},[1919,31179,1921],{},[1148,31181,2529],{},[1156,31183,1677],{},[1148,31185,5755],{},[1217,31187,31188,31190],{},[1156,31189,1677],{},[1919,31191,2780],{},[1172,31193,31194],{"encoding":1174},"H_1: \\mu > \\mu_0",[1482,31196,31197],{},"jednostranná",[1465,31199,31200,31203,31235],{},[1482,31201,31202],{},"menší",[1482,31204,31205],{},[1115,31206,31208],{"className":31207},[1136],[1138,31209,31210],{"xmlns":1140},[1142,31211,31212,31232],{},[1145,31213,31214,31220,31222,31224,31226],{},[1217,31215,31216,31218],{},[1156,31217,6797],{},[1919,31219,1921],{},[1148,31221,2529],{},[1156,31223,1677],{},[1148,31225,5682],{},[1217,31227,31228,31230],{},[1156,31229,1677],{},[1919,31231,2780],{},[1172,31233,31234],{"encoding":1174},"H_1: \\mu \u003C \\mu_0",[1482,31236,31197],{},[1818,31238,31240],{"id":31239},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,31242,31243],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1124,31245,31246,31283],{},[1127,31247,31248,31251,31252,31269,31270,1247],{},[1445,31249,31250],{},"Chyba I. druhu"," — zamítnutí ",[1115,31253,31255],{"className":31254},[1136],[1138,31256,31257],{"xmlns":1140},[1142,31258,31259,31267],{},[1145,31260,31261],{},[1217,31262,31263,31265],{},[1156,31264,6797],{},[1919,31266,2780],{},[1172,31268,6802],{"encoding":1174},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,31271,31273],{"className":31272},[1136],[1138,31274,31275],{"xmlns":1140},[1142,31276,31277,31281],{},[1145,31278,31279],{},[1156,31280,8567],{},[1172,31282,8630],{"encoding":1174},[1127,31284,31285,31288,31289,31306,31307,31324,31325,1247],{},[1445,31286,31287],{},"Chyba II. druhu"," — přijetí ",[1115,31290,31292],{"className":31291},[1136],[1138,31293,31294],{"xmlns":1140},[1142,31295,31296,31304],{},[1145,31297,31298],{},[1217,31299,31300,31302],{},[1156,31301,6797],{},[1919,31303,2780],{},[1172,31305,6802],{"encoding":1174},", ačkoliv platí ",[1115,31308,31310],{"className":31309},[1136],[1138,31311,31312],{"xmlns":1140},[1142,31313,31314,31322],{},[1145,31315,31316],{},[1217,31317,31318,31320],{},[1156,31319,6797],{},[1919,31321,1921],{},[1172,31323,8200],{"encoding":1174},". Pravděpodobnost ",[1115,31326,31328],{"className":31327},[1136],[1138,31329,31330],{"xmlns":1140},[1142,31331,31332,31336],{},[1145,31333,31334],{},[1156,31335,21449],{},[1172,31337,30837],{"encoding":1174},[1459,31339,31340,31403],{},[1462,31341,31342],{},[1465,31343,31344,31364,31383],{},[1468,31345,31346,31347],{},"Úsudek o ",[1115,31348,31350],{"className":31349},[1136],[1138,31351,31352],{"xmlns":1140},[1142,31353,31354,31362],{},[1145,31355,31356],{},[1217,31357,31358,31360],{},[1156,31359,6797],{},[1919,31361,2780],{},[1172,31363,6802],{"encoding":1174},[1468,31365,31366,13494],{},[1115,31367,31369],{"className":31368},[1136],[1138,31370,31371],{"xmlns":1140},[1142,31372,31373,31381],{},[1145,31374,31375],{},[1217,31376,31377,31379],{},[1156,31378,6797],{},[1919,31380,2780],{},[1172,31382,6802],{"encoding":1174},[1468,31384,31385,31402],{},[1115,31386,31388],{"className":31387},[1136],[1138,31389,31390],{"xmlns":1140},[1142,31391,31392,31400],{},[1145,31393,31394],{},[1217,31395,31396,31398],{},[1156,31397,6797],{},[1919,31399,2780],{},[1172,31401,6802],{"encoding":1174}," neplatí",[1477,31404,31405,31447],{},[1465,31406,31407,31410,31431],{},[1482,31408,31409],{},"Nezamítá se",[1482,31411,31412,31413],{},"správné rozhodnutí, ",[1115,31414,31416],{"className":31415},[1136],[1138,31417,31418],{"xmlns":1140},[1142,31419,31420,31428],{},[1145,31421,31422,31424,31426],{},[1919,31423,1921],{},[1148,31425,1990],{},[1156,31427,8567],{},[1172,31429,31430],{"encoding":1174},"1-\\alpha",[1482,31432,31433,31434],{},"chyba II. druhu, ",[1115,31435,31437],{"className":31436},[1136],[1138,31438,31439],{"xmlns":1140},[1142,31440,31441,31445],{},[1145,31442,31443],{},[1156,31444,21449],{},[1172,31446,30837],{"encoding":1174},[1465,31448,31449,31452,31468],{},[1482,31450,31451],{},"Zamítá se",[1482,31453,31454,31455],{},"chyba I. druhu, ",[1115,31456,31458],{"className":31457},[1136],[1138,31459,31460],{"xmlns":1140},[1142,31461,31462,31466],{},[1145,31463,31464],{},[1156,31465,8567],{},[1172,31467,8630],{"encoding":1174},[1482,31469,31412,31470],{},[1115,31471,31473],{"className":31472},[1136],[1138,31474,31475],{"xmlns":1140},[1142,31476,31477,31485],{},[1145,31478,31479,31481,31483],{},[1919,31480,1921],{},[1148,31482,1990],{},[1156,31484,21449],{},[1172,31486,31487],{"encoding":1174},"1-\\beta",[1110,31489,31490,6884,31493,31506],{},[1445,31491,31492],{},"Hladina významnosti",[1115,31494,31496],{"className":31495},[1136],[1138,31497,31498],{"xmlns":1140},[1142,31499,31500,31504],{},[1145,31501,31502],{},[1156,31503,8567],{},[1172,31505,8630],{"encoding":1174}," je předem pevně zvolená pravděpodobnost chyby I. druhu (klasicky 5 %). Testovací postup je odvozen tak, aby při dané hladině významnosti zajišťoval minimální pravděpodobnost chyby II. druhu.",[1110,31508,31509],{},[1527,31510],{"alt":31511,"className":31512,"src":31513},"mask-th-chyba-i-ii",[1531,1532],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,31515,31516,31517,31530,31531,31544,31545,31558,31559,7108,31572,31585,31586,1247],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,31518,31520],{"className":31519},[1136],[1138,31521,31522],{"xmlns":1140},[1142,31523,31524,31528],{},[1145,31525,31526],{},[1156,31527,1262],{},[1172,31529,1262],{"encoding":1174}," doleva zmenší ",[1115,31532,31534],{"className":31533},[1136],[1138,31535,31536],{"xmlns":1140},[1142,31537,31538,31542],{},[1145,31539,31540],{},[1156,31541,21449],{},[1172,31543,30837],{"encoding":1174},", ale zvětší ",[1115,31546,31548],{"className":31547},[1136],[1138,31549,31550],{"xmlns":1140},[1142,31551,31552,31556],{},[1145,31553,31554],{},[1156,31555,8567],{},[1172,31557,8630],{"encoding":1174},", a naopak. Pro danou hladinu ",[1115,31560,31562],{"className":31561},[1136],[1138,31563,31564],{"xmlns":1140},[1142,31565,31566,31570],{},[1145,31567,31568],{},[1156,31569,8567],{},[1172,31571,8630],{"encoding":1174},[1115,31573,31575],{"className":31574},[1136],[1138,31576,31577],{"xmlns":1140},[1142,31578,31579,31583],{},[1145,31580,31581],{},[1156,31582,1262],{},[1172,31584,1262],{"encoding":1174}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,31587,31589],{"className":31588},[1136],[1138,31590,31591],{"xmlns":1140},[1142,31592,31593,31601],{},[1145,31594,31595],{},[1217,31596,31597,31599],{},[1156,31598,6797],{},[1919,31600,2780],{},[1172,31602,6802],{"encoding":1174},[1818,31604,31606],{"id":31605},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,31608,31609,6884,31611,31624,31625,1247],{},[1445,31610,8204],{},[1115,31612,31614],{"className":31613},[1136],[1138,31615,31616],{"xmlns":1140},[1142,31617,31618,31622],{},[1145,31619,31620],{},[1156,31621,5427],{},[1172,31623,5427],{"encoding":1174}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,31626,31628],{"className":31627},[1136],[1138,31629,31630],{"xmlns":1140},[1142,31631,31632,31640],{},[1145,31633,31634],{},[1217,31635,31636,31638],{},[1156,31637,6797],{},[1919,31639,2780],{},[1172,31641,6802],{"encoding":1174},[1110,31643,31644,6884,31647,31660,31661,31678],{},[1445,31645,31646],{},"Kritický obor",[1115,31648,31650],{"className":31649},[1136],[1138,31651,31652],{"xmlns":1140},[1142,31653,31654,31658],{},[1145,31655,31656],{},[1156,31657,6835],{},[1172,31659,6835],{"encoding":1174}," je množina hodnot svědčících pro ",[1115,31662,31664],{"className":31663},[1136],[1138,31665,31666],{"xmlns":1140},[1142,31667,31668,31676],{},[1145,31669,31670],{},[1217,31671,31672,31674],{},[1156,31673,6797],{},[1919,31675,1921],{},[1172,31677,8200],{"encoding":1174},". Je zkonstruován tak, aby",[1115,31680,31682],{"className":31681},[1136],[1138,31683,31684],{"xmlns":1140,"display":1897},[1142,31685,31686,31714],{},[1145,31687,31688,31690,31692,31694,31696,31698,31700,31706,31708,31710,31712],{},[1156,31689,5126],{},[1148,31691,1151],{"stretchy":1150},[1156,31693,5427],{},[1148,31695,12164],{},[1156,31697,6835],{},[1148,31699,3636],{},[1217,31701,31702,31704],{},[1156,31703,6797],{},[1919,31705,2780],{},[1148,31707,1170],{"stretchy":1150},[1148,31709,1914],{},[1156,31711,8567],{},[1148,31713,1164],{"separator":1121},[1172,31715,31716],{"encoding":1174},"P(T \\in W \\mid H_0) = \\alpha,",[1110,31718,31719,31720,31733,31734,31751],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,31721,31723],{"className":31722},[1136],[1138,31724,31725],{"xmlns":1140},[1142,31726,31727,31731],{},[1145,31728,31729],{},[1156,31730,6835],{},[1172,31732,6835],{"encoding":1174}," i při platné ",[1115,31735,31737],{"className":31736},[1136],[1138,31738,31739],{"xmlns":1140},[1142,31740,31741,31749],{},[1145,31742,31743],{},[1217,31744,31745,31747],{},[1156,31746,6797],{},[1919,31748,2780],{},[1172,31750,6802],{"encoding":1174},", byla rovna zvolené hladině významnosti.",[1818,31753,31755],{"id":31754},"postup-testování-hypotézy","Postup testování hypotézy",[1110,31757,31758],{},[1527,31759],{"alt":31760,"className":31761,"src":31762},"mask-ilu-postup-testovani",[1531,1532],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[1538,31764,31765,31802,31805,31821],{},[1127,31766,31767,31768,1204,31785,1247],{},"Formulace hypotéz ",[1115,31769,31771],{"className":31770},[1136],[1138,31772,31773],{"xmlns":1140},[1142,31774,31775,31783],{},[1145,31776,31777],{},[1217,31778,31779,31781],{},[1156,31780,6797],{},[1919,31782,2780],{},[1172,31784,6802],{"encoding":1174},[1115,31786,31788],{"className":31787},[1136],[1138,31789,31790],{"xmlns":1140},[1142,31791,31792,31800],{},[1145,31793,31794],{},[1217,31795,31796,31798],{},[1156,31797,6797],{},[1919,31799,1921],{},[1172,31801,8200],{"encoding":1174},[1127,31803,31804],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1127,31806,31807,31808,1247],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,31809,31811],{"className":31810},[1136],[1138,31812,31813],{"xmlns":1140},[1142,31814,31815,31819],{},[1145,31816,31817],{},[1156,31818,6835],{},[1172,31820,6835],{"encoding":1174},[1127,31822,31823,31824],{},"Formulace závěru:\n",[1124,31825,31826,31904],{},[1127,31827,31828,31829,4984,31847,31864,31865,31885,31886,31903],{},"pokud ",[1115,31830,31832],{"className":31831},[1136],[1138,31833,31834],{"xmlns":1140},[1142,31835,31836,31844],{},[1145,31837,31838,31840,31842],{},[1156,31839,5427],{},[1148,31841,12164],{},[1156,31843,6835],{},[1172,31845,31846],{"encoding":1174},"T \\in W",[1115,31848,31850],{"className":31849},[1136],[1138,31851,31852],{"xmlns":1140},[1142,31853,31854,31862],{},[1145,31855,31856],{},[1217,31857,31858,31860],{},[1156,31859,6797],{},[1919,31861,1921],{},[1172,31863,8200],{"encoding":1174}," je testem prokázána na hladině významnosti ",[1115,31866,31868],{"className":31867},[1136],[1138,31869,31870],{"xmlns":1140},[1142,31871,31872,31882],{},[1145,31873,31874,31876,31878,31880],{},[1919,31875,5001],{},[1156,31877,8567],{},[5009,31879,5011],{},[1156,31881,5014],{"mathvariant":2014},[1172,31883,31884],{"encoding":1174},"100\\alpha\\,\\%"," (zamítáme ",[1115,31887,31889],{"className":31888},[1136],[1138,31890,31891],{"xmlns":1140},[1142,31892,31893,31901],{},[1145,31894,31895],{},[1217,31896,31897,31899],{},[1156,31898,6797],{},[1919,31900,2780],{},[1172,31902,6802],{"encoding":1174},");",[1127,31905,31828,31906,4984,31925,31942,31943,31962,31963,31980],{},[1115,31907,31909],{"className":31908},[1136],[1138,31910,31911],{"xmlns":1140},[1142,31912,31913,31922],{},[1145,31914,31915,31917,31920],{},[1156,31916,5427],{},[1148,31918,31919],{"mathvariant":2014},"∉",[1156,31921,6835],{},[1172,31923,31924],{"encoding":1174},"T \\notin W",[1115,31926,31928],{"className":31927},[1136],[1138,31929,31930],{"xmlns":1140},[1142,31931,31932,31940],{},[1145,31933,31934],{},[1217,31935,31936,31938],{},[1156,31937,6797],{},[1919,31939,1921],{},[1172,31941,8200],{"encoding":1174}," není testem prokázána na hladině významnosti ",[1115,31944,31946],{"className":31945},[1136],[1138,31947,31948],{"xmlns":1140},[1142,31949,31950,31960],{},[1145,31951,31952,31954,31956,31958],{},[1919,31953,5001],{},[1156,31955,8567],{},[5009,31957,5011],{},[1156,31959,5014],{"mathvariant":2014},[1172,31961,31884],{"encoding":1174}," ; ",[1115,31964,31966],{"className":31965},[1136],[1138,31967,31968],{"xmlns":1140},[1142,31969,31970,31978],{},[1145,31971,31972],{},[1217,31973,31974,31976],{},[1156,31975,6797],{},[1919,31977,2780],{},[1172,31979,6802],{"encoding":1174}," nezamítáme.",[1110,31982,31983,31984,31987,31988,32005,32006,32023,32024,32044,32045,5832,32062,6884,32082,32099],{},"Rovnocennou alternativou je ",[1445,31985,31986],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,31989,31991],{"className":31990},[1136],[1138,31992,31993],{"xmlns":1140},[1142,31994,31995,32003],{},[1145,31996,31997],{},[1217,31998,31999,32001],{},[1156,32000,6797],{},[1919,32002,2780],{},[1172,32004,6802],{"encoding":1174},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,32007,32009],{"className":32008},[1136],[1138,32010,32011],{"xmlns":1140},[1142,32012,32013,32021],{},[1145,32014,32015],{},[1217,32016,32017,32019],{},[1156,32018,6797],{},[1919,32020,2780],{},[1172,32022,6802],{"encoding":1174},". Rozhodovací pravidlo: ",[1115,32025,32027],{"className":32026},[1136],[1138,32028,32029],{"xmlns":1140},[1142,32030,32031,32041],{},[1145,32032,32033,32035,32037,32039],{},[1156,32034,1110],{},[1148,32036,11884],{},[1156,32038,8567],{},[1148,32040,12693],{},[1172,32042,32043],{"encoding":1174},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,32046,32048],{"className":32047},[1136],[1138,32049,32050],{"xmlns":1140},[1142,32051,32052,32060],{},[1145,32053,32054],{},[1217,32055,32056,32058],{},[1156,32057,6797],{},[1919,32059,2780],{},[1172,32061,6802],{"encoding":1174},[1115,32063,32065],{"className":32064},[1136],[1138,32066,32067],{"xmlns":1140},[1142,32068,32069,32079],{},[1145,32070,32071,32073,32075,32077],{},[1156,32072,1110],{},[1148,32074,5755],{},[1156,32076,8567],{},[1148,32078,12693],{},[1172,32080,32081],{"encoding":1174},"p > \\alpha \\Rightarrow",[1115,32083,32085],{"className":32084},[1136],[1138,32086,32087],{"xmlns":1140},[1142,32088,32089,32097],{},[1145,32090,32091],{},[1217,32092,32093,32095],{},[1156,32094,6797],{},[1919,32096,2780],{},[1172,32098,6802],{"encoding":1174}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1437,32101,32103],{"id":32102},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,32105,32106,32107,32120,32121,32153,32154,32167,32168,1204,32185,32202,32203,32221,32222,32235],{},"Test o střední hodnotě ",[1115,32108,32110],{"className":32109},[1136],[1138,32111,32112],{"xmlns":1140},[1142,32113,32114,32118],{},[1145,32115,32116],{},[1156,32117,1677],{},[1172,32119,1680],{"encoding":1174}," rozdělení ",[1115,32122,32124],{"className":32123},[1136],[1138,32125,32126],{"xmlns":1140},[1142,32127,32128,32150],{},[1145,32129,32130,32132,32134,32136,32138,32140,32142,32148],{},[1156,32131,2168],{},[1148,32133,14325],{},[1156,32135,12034],{},[1148,32137,1151],{"stretchy":1150},[1156,32139,1677],{},[1148,32141,1164],{"separator":1121},[5465,32143,32144,32146],{},[1156,32145,1693],{},[1919,32147,2302],{},[1148,32149,1170],{"stretchy":1150},[1172,32151,32152],{"encoding":1174},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,32155,32157],{"className":32156},[1136],[1138,32158,32159],{"xmlns":1140},[1142,32160,32161,32165],{},[1145,32162,32163],{},[1156,32164,1292],{},[1172,32166,1292],{"encoding":1174}," se určí charakteristiky ",[1115,32169,32171],{"className":32170},[1136],[1138,32172,32173],{"xmlns":1140},[1142,32174,32175,32183],{},[1145,32176,32177],{},[1153,32178,32179,32181],{"accent":1121},[1156,32180,1158],{},[1148,32182,1161],{},[1172,32184,2136],{"encoding":1174},[1115,32186,32188],{"className":32187},[1136],[1138,32189,32190],{"xmlns":1140},[1142,32191,32192,32200],{},[1145,32193,32194],{},[5465,32195,32196,32198],{},[1156,32197,1198],{},[1919,32199,2302],{},[1172,32201,20888],{"encoding":1174},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,32204,32206],{"className":32205},[1136],[1138,32207,32208],{"xmlns":1140},[1142,32209,32210,32218],{},[1145,32211,32212],{},[1217,32213,32214,32216],{},[1156,32215,1677],{},[1919,32217,2780],{},[1172,32219,32220],{"encoding":1174},"\\mu_0"," a neznámou hodnotou ",[1115,32223,32225],{"className":32224},[1136],[1138,32226,32227],{"xmlns":1140},[1142,32228,32229,32233],{},[1145,32230,32231],{},[1156,32232,1677],{},[1172,32234,1680],{"encoding":1174},". Testové kritérium",[1115,32237,32239],{"className":32238},[1136],[1138,32240,32241],{"xmlns":1140,"display":1897},[1142,32242,32243,32287],{},[1145,32244,32245,32247,32249,32269,32273,32275],{},[1156,32246,5427],{},[1148,32248,1914],{},[1916,32250,32251,32267],{},[1145,32252,32253,32259,32261],{},[1153,32254,32255,32257],{"accent":1121},[1156,32256,1158],{},[1148,32258,1161],{},[1148,32260,1990],{},[1217,32262,32263,32265],{},[1156,32264,1677],{},[1919,32266,2780],{},[1156,32268,1198],{},[5460,32270,32271],{},[1156,32272,1292],{},[1148,32274,14325],{},[1217,32276,32277,32279],{},[1156,32278,12288],{},[1145,32280,32281,32283,32285],{},[1156,32282,1292],{},[1148,32284,1990],{},[1919,32286,1921],{},[1172,32288,32289],{"encoding":1174},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,32291,32292,32293,32311],{},"má Studentovo rozdělení o ",[1115,32294,32296],{"className":32295},[1136],[1138,32297,32298],{"xmlns":1140},[1142,32299,32300,32308],{},[1145,32301,32302,32304,32306],{},[1156,32303,1292],{},[1148,32305,1990],{},[1919,32307,1921],{},[1172,32309,32310],{"encoding":1174},"n-1"," stupních volnosti.",[1459,32313,32314,32372],{},[1462,32315,32316],{},[1465,32317,32318,32337,32356],{},[1468,32319,32320],{},[1115,32321,32323],{"className":32322},[1136],[1138,32324,32325],{"xmlns":1140},[1142,32326,32327,32335],{},[1145,32328,32329],{},[1217,32330,32331,32333],{},[1156,32332,6797],{},[1919,32334,2780],{},[1172,32336,6802],{"encoding":1174},[1468,32338,32339],{},[1115,32340,32342],{"className":32341},[1136],[1138,32343,32344],{"xmlns":1140},[1142,32345,32346,32354],{},[1145,32347,32348],{},[1217,32349,32350,32352],{},[1156,32351,6797],{},[1919,32353,1921],{},[1172,32355,8200],{"encoding":1174},[1468,32357,32358,32359],{},"Kritický obor ",[1115,32360,32362],{"className":32361},[1136],[1138,32363,32364],{"xmlns":1140},[1142,32365,32366,32370],{},[1145,32367,32368],{},[1156,32369,6835],{},[1172,32371,6835],{"encoding":1174},[1477,32373,32374,32464,32562],{},[1465,32375,32376,32400,32424],{},[1482,32377,32378],{},[1115,32379,32381],{"className":32380},[1136],[1138,32382,32383],{"xmlns":1140},[1142,32384,32385,32397],{},[1145,32386,32387,32389,32391],{},[1156,32388,1677],{},[1148,32390,11884],{},[1217,32392,32393,32395],{},[1156,32394,1677],{},[1919,32396,2780],{},[1172,32398,32399],{"encoding":1174},"\\mu \\le \\mu_0",[1482,32401,32402],{},[1115,32403,32405],{"className":32404},[1136],[1138,32406,32407],{"xmlns":1140},[1142,32408,32409,32421],{},[1145,32410,32411,32413,32415],{},[1156,32412,1677],{},[1148,32414,5755],{},[1217,32416,32417,32419],{},[1156,32418,1677],{},[1919,32420,2780],{},[1172,32422,32423],{"encoding":1174},"\\mu > \\mu_0",[1482,32425,32426],{},[1115,32427,32429],{"className":32428},[1136],[1138,32430,32431],{"xmlns":1140},[1142,32432,32433,32461],{},[1145,32434,32435,32437,32439,32451,32453,32455,32457,32459],{},[1156,32436,12288],{},[1148,32438,8553],{},[1217,32440,32441,32443],{},[1156,32442,12288],{},[1145,32444,32445,32447,32449],{},[1919,32446,1921],{},[1148,32448,1990],{},[1156,32450,8567],{},[1148,32452,1151],{"stretchy":1150},[1156,32454,1292],{},[1148,32456,1990],{},[1919,32458,1921],{},[1148,32460,1170],{"stretchy":1150},[1172,32462,32463],{"encoding":1174},"t \\ge t_{1-\\alpha}(n-1)",[1465,32465,32466,32490,32514],{},[1482,32467,32468],{},[1115,32469,32471],{"className":32470},[1136],[1138,32472,32473],{"xmlns":1140},[1142,32474,32475,32487],{},[1145,32476,32477,32479,32481],{},[1156,32478,1677],{},[1148,32480,1914],{},[1217,32482,32483,32485],{},[1156,32484,1677],{},[1919,32486,2780],{},[1172,32488,32489],{"encoding":1174},"\\mu = \\mu_0",[1482,32491,32492],{},[1115,32493,32495],{"className":32494},[1136],[1138,32496,32497],{"xmlns":1140},[1142,32498,32499,32511],{},[1145,32500,32501,32503,32505],{},[1156,32502,1677],{},[1148,32504,16087],{"mathvariant":2014},[1217,32506,32507,32509],{},[1156,32508,1677],{},[1919,32510,2780],{},[1172,32512,32513],{"encoding":1174},"\\mu \\neq \\mu_0",[1482,32515,32516],{},[1115,32517,32519],{"className":32518},[1136],[1138,32520,32521],{"xmlns":1140},[1142,32522,32523,32559],{},[1145,32524,32525,32527,32529,32531,32533,32549,32551,32553,32555,32557],{},[1148,32526,3636],{"stretchy":1150},[1156,32528,12288],{},[1148,32530,3636],{"stretchy":1150},[1148,32532,8553],{},[1217,32534,32535,32537],{},[1156,32536,12288],{},[1145,32538,32539,32541,32543,32545,32547],{},[1919,32540,1921],{},[1148,32542,1990],{},[1156,32544,8567],{},[1156,32546,4412],{"mathvariant":2014},[1919,32548,2302],{},[1148,32550,1151],{"stretchy":1150},[1156,32552,1292],{},[1148,32554,1990],{},[1919,32556,1921],{},[1148,32558,1170],{"stretchy":1150},[1172,32560,32561],{"encoding":1174},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1465,32563,32564,32588,32612],{},[1482,32565,32566],{},[1115,32567,32569],{"className":32568},[1136],[1138,32570,32571],{"xmlns":1140},[1142,32572,32573,32585],{},[1145,32574,32575,32577,32579],{},[1156,32576,1677],{},[1148,32578,8553],{},[1217,32580,32581,32583],{},[1156,32582,1677],{},[1919,32584,2780],{},[1172,32586,32587],{"encoding":1174},"\\mu \\ge \\mu_0",[1482,32589,32590],{},[1115,32591,32593],{"className":32592},[1136],[1138,32594,32595],{"xmlns":1140},[1142,32596,32597,32609],{},[1145,32598,32599,32601,32603],{},[1156,32600,1677],{},[1148,32602,5682],{},[1217,32604,32605,32607],{},[1156,32606,1677],{},[1919,32608,2780],{},[1172,32610,32611],{"encoding":1174},"\\mu \u003C \\mu_0",[1482,32613,32614],{},[1115,32615,32617],{"className":32616},[1136],[1138,32618,32619],{"xmlns":1140},[1142,32620,32621,32651],{},[1145,32622,32623,32625,32627,32629,32641,32643,32645,32647,32649],{},[1156,32624,12288],{},[1148,32626,11884],{},[1148,32628,1990],{},[1217,32630,32631,32633],{},[1156,32632,12288],{},[1145,32634,32635,32637,32639],{},[1919,32636,1921],{},[1148,32638,1990],{},[1156,32640,8567],{},[1148,32642,1151],{"stretchy":1150},[1156,32644,1292],{},[1148,32646,1990],{},[1919,32648,1921],{},[1148,32650,1170],{"stretchy":1150},[1172,32652,32653],{"encoding":1174},"t \\le -t_{1-\\alpha}(n-1)",[1110,32655,32656,32657,32660],{},"V R test provádí ",[1434,32658,32659],{},"t.test()",". Autobusová linka měla na trase průměrnou dobu jízdy 12 minut; po úpravě trasy se při devíti jízdách naměřily časy v minutách. Ovlivnila úprava trasy dobu jízdy?",[3261,32662,32664],{"className":3263,"code":32663,"language":71,"meta":3265,"style":3265},"x \u003C- c(12.5, 13.5, 11.9, 12.2, 13.0, 14.3, 12.2, 11.8, 14.0)\nt.test(x, mu = 12, alternative = \"two.sided\")\n",[1434,32665,32666,32720],{"__ignoreMap":3265},[1115,32667,32668,32670,32672,32674,32676,32679,32681,32684,32686,32689,32691,32694,32696,32699,32701,32704,32706,32708,32710,32713,32715,32718],{"class":3270,"line":10},[1115,32669,1158],{"class":3280},[1115,32671,3291],{"class":3273},[1115,32673,4142],{"class":3294},[1115,32675,1151],{"class":3277},[1115,32677,32678],{"class":3312},"12.5",[1115,32680,1164],{"class":3273},[1115,32682,32683],{"class":3312}," 13.5",[1115,32685,1164],{"class":3273},[1115,32687,32688],{"class":3312}," 11.9",[1115,32690,1164],{"class":3273},[1115,32692,32693],{"class":3312}," 12.2",[1115,32695,1164],{"class":3273},[1115,32697,32698],{"class":3312}," 13.0",[1115,32700,1164],{"class":3273},[1115,32702,32703],{"class":3312}," 14.3",[1115,32705,1164],{"class":3273},[1115,32707,32693],{"class":3312},[1115,32709,1164],{"class":3273},[1115,32711,32712],{"class":3312}," 11.8",[1115,32714,1164],{"class":3273},[1115,32716,32717],{"class":3312}," 14.0",[1115,32719,3283],{"class":3277},[1115,32721,32722,32725,32727,32729,32731,32733,32735,32737,32739,32742,32744,32747],{"class":3270,"line":27},[1115,32723,32724],{"class":3294},"t.test",[1115,32726,1151],{"class":3277},[1115,32728,1158],{"class":3280},[1115,32730,1164],{"class":3273},[1115,32732,6241],{"class":3280},[1115,32734,3309],{"class":3273},[1115,32736,8919],{"class":3312},[1115,32738,1164],{"class":3273},[1115,32740,32741],{"class":3280}," alternative",[1115,32743,3309],{"class":3273},[1115,32745,32746],{"class":3300}," \"two.sided\"",[1115,32748,3283],{"class":3277},[3261,32750,32753],{"className":32751,"code":32752,"language":4279,"meta":3265},[4277],"    One Sample t-test\n\ndata:  x\nt = 2.6685, df = 8, p-value = 0.02843\nalternative hypothesis: true mean is not equal to 12\n95 percent confidence interval:\n 12.11169 13.53275\nsample estimates:\nmean of x \n 12.82222 \n",[1434,32754,32752],{"__ignoreMap":3265},[1110,32756,32757,32759,32760,32763,32764,32767,32768,32771,32772,32795],{},[1434,32758,12288],{}," je testové kritérium, ",[1434,32761,32762],{},"df"," stupně volnosti, ",[1434,32765,32766],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[1434,32769,32770],{},"mean of x"," výběrový průměr. Zde ",[1115,32773,32775],{"className":32774},[1136],[1138,32776,32777],{"xmlns":1140},[1142,32778,32779,32792],{},[1145,32780,32781,32783,32785,32788,32790],{},[1156,32782,1110],{},[1148,32784,1914],{},[1919,32786,32787],{},"0,02843",[1148,32789,5682],{},[1919,32791,9160],{},[1172,32793,32794],{"encoding":1174},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,32797,32799,32806,32894,32950,33042],{"className":32798,"dataCallout":2145},[1106,2144],[1110,32800,32802,32805],{"className":32801},[1113],[1115,32803],{"className":32804,"ariaHidden":1121},[1118,2152,1120],"Příklad: Kontrola objemu lahví",[1110,32807,32808,32809,32831,32832,32850,32851,32874,32875,32893],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,32810,32812],{"className":32811},[1136],[1138,32813,32814],{"xmlns":1140},[1142,32815,32816,32828],{},[1145,32817,32818,32824,32826],{},[1217,32819,32820,32822],{},[1156,32821,1677],{},[1919,32823,2780],{},[1148,32825,1914],{},[1919,32827,13600],{},[1172,32829,32830],{"encoding":1174},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,32833,32835],{"className":32834},[1136],[1138,32836,32837],{"xmlns":1140},[1142,32838,32839,32847],{},[1145,32840,32841,32843,32845],{},[1156,32842,1292],{},[1148,32844,1914],{},[1919,32846,2187],{},[1172,32848,32849],{"encoding":1174},"n = 20"," lahví dal ",[1115,32852,32854],{"className":32853},[1136],[1138,32855,32856],{"xmlns":1140},[1142,32857,32858,32871],{},[1145,32859,32860,32866,32868],{},[1153,32861,32862,32864],{"accent":1121},[1156,32863,1158],{},[1148,32865,1161],{},[1148,32867,1914],{},[1919,32869,32870],{},"0,492",[1172,32872,32873],{"encoding":1174},"\\bar{x} = 0{,}492"," l, ",[1115,32876,32878],{"className":32877},[1136],[1138,32879,32880],{"xmlns":1140},[1142,32881,32882,32890],{},[1145,32883,32884,32886,32888],{},[1156,32885,1198],{},[1148,32887,1914],{},[1919,32889,19908],{},[1172,32891,32892],{"encoding":1174},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,32895,32896,32922,32923,32949],{},[1115,32897,32899],{"className":32898},[1136],[1138,32900,32901],{"xmlns":1140},[1142,32902,32903,32919],{},[1145,32904,32905,32911,32913,32915,32917],{},[1217,32906,32907,32909],{},[1156,32908,6797],{},[1919,32910,2780],{},[1148,32912,2529],{},[1156,32914,1677],{},[1148,32916,8553],{},[1919,32918,13600],{},[1172,32920,32921],{"encoding":1174},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,32924,32926],{"className":32925},[1136],[1138,32927,32928],{"xmlns":1140},[1142,32929,32930,32946],{},[1145,32931,32932,32938,32940,32942,32944],{},[1217,32933,32934,32936],{},[1156,32935,6797],{},[1919,32937,1921],{},[1148,32939,2529],{},[1156,32941,1677],{},[1148,32943,5682],{},[1919,32945,13600],{},[1172,32947,32948],{"encoding":1174},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,32951,32952],{},[1115,32953,32955],{"className":32954},[1136],[1138,32956,32957],{"xmlns":1140},[1142,32958,32959,33039],{},[1145,32960,32961,32963,32965,32977,32981,32983,32985,32988,32990,32992,32994,32996,32998,33000,33002,33004,33016,33018,33020,33022,33024,33026,33028,33030,33032,33034,33037],{},[1156,32962,12288],{},[1148,32964,1914],{},[1916,32966,32967,32975],{},[1145,32968,32969,32971,32973],{},[1919,32970,32870],{},[1148,32972,1990],{},[1919,32974,13600],{},[1919,32976,19908],{},[5460,32978,32979],{},[1919,32980,2187],{},[1148,32982,1914],{},[1148,32984,1990],{},[1919,32986,32987],{},"2,385",[1148,32989,1164],{"separator":1121},[1954,32991],{"width":1956},[1156,32993,6835],{},[1148,32995,1914],{},[1148,32997,8536],{"stretchy":1150},[1156,32999,12288],{},[1148,33001,11884],{},[1148,33003,1990],{},[1217,33005,33006,33008],{},[1156,33007,12288],{},[1145,33009,33010,33012,33014],{},[1919,33011,2780],{},[1148,33013,1164],{"separator":1121},[1919,33015,2378],{},[1148,33017,1151],{"stretchy":1150},[1919,33019,2464],{},[1148,33021,1170],{"stretchy":1150},[1148,33023,8596],{"stretchy":1150},[1148,33025,1914],{},[1148,33027,8536],{"stretchy":1150},[1156,33029,12288],{},[1148,33031,11884],{},[1148,33033,1990],{},[1919,33035,33036],{},"1,729",[1148,33038,8596],{"stretchy":1150},[1172,33040,33041],{"encoding":1174},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,33043,33044,33045,11165,33063,33080],{},"Protože ",[1115,33046,33048],{"className":33047},[1136],[1138,33049,33050],{"xmlns":1140},[1142,33051,33052,33060],{},[1145,33053,33054,33056,33058],{},[1156,33055,12288],{},[1148,33057,12164],{},[1156,33059,6835],{},[1172,33061,33062],{"encoding":1174},"t \\in W",[1115,33064,33066],{"className":33065},[1136],[1138,33067,33068],{"xmlns":1140},[1142,33069,33070,33078],{},[1145,33071,33072],{},[1217,33073,33074,33076],{},[1156,33075,6797],{},[1919,33077,2780],{},[1172,33079,6802],{"encoding":1174},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,33082,33083,33084,33086,33087,2529],{},"Ze souhrnných charakteristik bez surových dat ",[1434,33085,32659],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[1434,33088,33089],{},"qt()",[3261,33091,33093],{"className":3263,"code":33092,"language":71,"meta":3265,"style":3265},"xbar \u003C- 0.492; s \u003C- 0.015; n \u003C- 20; mu0 \u003C- 0.5\nt \u003C- (xbar - mu0) \u002F s * sqrt(n)\nt_krit \u003C- qt(0.05, df = n - 1)\nt\nt_krit\n",[1434,33094,33095,33133,33165,33195,33200],{"__ignoreMap":3265},[1115,33096,33097,33100,33102,33105,33107,33109,33111,33114,33116,33118,33120,33123,33125,33128,33130],{"class":3270,"line":10},[1115,33098,33099],{"class":3280},"xbar",[1115,33101,3291],{"class":3273},[1115,33103,33104],{"class":3312}," 0.492",[1115,33106,5832],{"class":3277},[1115,33108,1198],{"class":3280},[1115,33110,3291],{"class":3273},[1115,33112,33113],{"class":3312}," 0.015",[1115,33115,5832],{"class":3277},[1115,33117,1292],{"class":3280},[1115,33119,3291],{"class":3273},[1115,33121,33122],{"class":3312}," 20",[1115,33124,5832],{"class":3277},[1115,33126,33127],{"class":3280},"mu0",[1115,33129,3291],{"class":3273},[1115,33131,33132],{"class":3312}," 0.5\n",[1115,33134,33135,33137,33139,33141,33143,33145,33148,33150,33152,33155,33157,33159,33161,33163],{"class":3270,"line":27},[1115,33136,12288],{"class":3280},[1115,33138,3291],{"class":3273},[1115,33140,6173],{"class":3277},[1115,33142,33099],{"class":3280},[1115,33144,6178],{"class":3273},[1115,33146,33147],{"class":3280}," mu0",[1115,33149,6207],{"class":3277},[1115,33151,4412],{"class":3273},[1115,33153,33154],{"class":3280}," s",[1115,33156,6216],{"class":3273},[1115,33158,6158],{"class":3294},[1115,33160,1151],{"class":3277},[1115,33162,1292],{"class":3280},[1115,33164,3283],{"class":3277},[1115,33166,33167,33170,33172,33175,33177,33180,33182,33184,33186,33189,33191,33193],{"class":3270,"line":148},[1115,33168,33169],{"class":3280},"t_krit",[1115,33171,3291],{"class":3273},[1115,33173,33174],{"class":3294}," qt",[1115,33176,1151],{"class":3277},[1115,33178,33179],{"class":3312},"0.05",[1115,33181,1164],{"class":3273},[1115,33183,15941],{"class":3280},[1115,33185,3309],{"class":3273},[1115,33187,33188],{"class":3280}," n",[1115,33190,6178],{"class":3273},[1115,33192,3882],{"class":3312},[1115,33194,3283],{"class":3277},[1115,33196,33197],{"class":3270,"line":111},[1115,33198,33199],{"class":3280},"t\n",[1115,33201,33202],{"class":3270,"line":96},[1115,33203,33204],{"class":3280},"t_krit\n",[3261,33206,33209],{"className":33207,"code":33208,"language":4279,"meta":3265},[4277],"[1] -2.385139\n[1] -1.729133\n",[1434,33210,33208],{"__ignoreMap":3265},[1110,33212,33213],{},[1527,33214],{"alt":33215,"className":33216,"src":33217},"mask-th-t-jednostranny",[1531,1532],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,33219,33220,33221,2529],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[1434,33222,32659],{},[1110,33224,33225,33228],{},[1445,33226,33227],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3261,33230,33232],{"className":3263,"code":33231,"language":71,"meta":3265,"style":3265},"x2 \u003C- c(9.5, 10.5, 8.9, 9.2, 10.0, 8.5, 9.2, 8.8, 10.0, 9.5, 9.2)\nt.test(x2, mu = 10, alternative = \"two.sided\")\n",[1434,33233,33234,33297],{"__ignoreMap":3265},[1115,33235,33236,33239,33241,33243,33245,33248,33250,33253,33255,33258,33260,33263,33265,33268,33270,33273,33275,33277,33279,33282,33284,33286,33288,33291,33293,33295],{"class":3270,"line":10},[1115,33237,33238],{"class":3280},"x2",[1115,33240,3291],{"class":3273},[1115,33242,4142],{"class":3294},[1115,33244,1151],{"class":3277},[1115,33246,33247],{"class":3312},"9.5",[1115,33249,1164],{"class":3273},[1115,33251,33252],{"class":3312}," 10.5",[1115,33254,1164],{"class":3273},[1115,33256,33257],{"class":3312}," 8.9",[1115,33259,1164],{"class":3273},[1115,33261,33262],{"class":3312}," 9.2",[1115,33264,1164],{"class":3273},[1115,33266,33267],{"class":3312}," 10.0",[1115,33269,1164],{"class":3273},[1115,33271,33272],{"class":3312}," 8.5",[1115,33274,1164],{"class":3273},[1115,33276,33262],{"class":3312},[1115,33278,1164],{"class":3273},[1115,33280,33281],{"class":3312}," 8.8",[1115,33283,1164],{"class":3273},[1115,33285,33267],{"class":3312},[1115,33287,1164],{"class":3273},[1115,33289,33290],{"class":3312}," 9.5",[1115,33292,1164],{"class":3273},[1115,33294,33262],{"class":3312},[1115,33296,3283],{"class":3277},[1115,33298,33299,33301,33303,33305,33307,33309,33311,33313,33315,33317,33319,33321],{"class":3270,"line":27},[1115,33300,32724],{"class":3294},[1115,33302,1151],{"class":3277},[1115,33304,33238],{"class":3280},[1115,33306,1164],{"class":3273},[1115,33308,6241],{"class":3280},[1115,33310,3309],{"class":3273},[1115,33312,14616],{"class":3312},[1115,33314,1164],{"class":3273},[1115,33316,32741],{"class":3280},[1115,33318,3309],{"class":3273},[1115,33320,32746],{"class":3300},[1115,33322,3283],{"class":3277},[3261,33324,33327],{"className":33325,"code":33326,"language":4279,"meta":3265},[4277],"    One Sample t-test\n\ndata:  x2\nt = -3.42, df = 10, p-value = 0.006548\nalternative hypothesis: true mean is not equal to 10\n95 percent confidence interval:\n 8.994081 9.787737\nsample estimates:\nmean of x \n 9.390909 \n",[1434,33328,33326],{"__ignoreMap":3265},[1110,33330,33331,33354],{},[1115,33332,33334],{"className":33333},[1136],[1138,33335,33336],{"xmlns":1140},[1142,33337,33338,33351],{},[1145,33339,33340,33342,33344,33347,33349],{},[1156,33341,1110],{},[1148,33343,1914],{},[1919,33345,33346],{},"0,006548",[1148,33348,5682],{},[1919,33350,9160],{},[1172,33352,33353],{"encoding":1174},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,33356,33357,33360],{},[1445,33358,33359],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3261,33362,33364],{"className":3263,"code":33363,"language":71,"meta":3265,"style":3265},"x3 \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)\nt.test(x3, mu = 4, alternative = \"two.sided\")\nshapiro.test(x3)\n",[1434,33365,33366,33417,33443],{"__ignoreMap":3265},[1115,33367,33368,33371,33373,33375,33377,33379,33381,33383,33385,33387,33389,33391,33393,33395,33397,33399,33401,33403,33405,33407,33409,33411,33413,33415],{"class":3270,"line":10},[1115,33369,33370],{"class":3280},"x3",[1115,33372,3291],{"class":3273},[1115,33374,4142],{"class":3294},[1115,33376,1151],{"class":3277},[1115,33378,17110],{"class":3312},[1115,33380,1164],{"class":3273},[1115,33382,17115],{"class":3312},[1115,33384,1164],{"class":3273},[1115,33386,17120],{"class":3312},[1115,33388,1164],{"class":3273},[1115,33390,17125],{"class":3312},[1115,33392,1164],{"class":3273},[1115,33394,17120],{"class":3312},[1115,33396,1164],{"class":3273},[1115,33398,17120],{"class":3312},[1115,33400,1164],{"class":3273},[1115,33402,17138],{"class":3312},[1115,33404,1164],{"class":3273},[1115,33406,17143],{"class":3312},[1115,33408,1164],{"class":3273},[1115,33410,17115],{"class":3312},[1115,33412,1164],{"class":3273},[1115,33414,17115],{"class":3312},[1115,33416,3283],{"class":3277},[1115,33418,33419,33421,33423,33425,33427,33429,33431,33433,33435,33437,33439,33441],{"class":3270,"line":27},[1115,33420,32724],{"class":3294},[1115,33422,1151],{"class":3277},[1115,33424,33370],{"class":3280},[1115,33426,1164],{"class":3273},[1115,33428,6241],{"class":3280},[1115,33430,3309],{"class":3273},[1115,33432,4184],{"class":3312},[1115,33434,1164],{"class":3273},[1115,33436,32741],{"class":3280},[1115,33438,3309],{"class":3273},[1115,33440,32746],{"class":3300},[1115,33442,3283],{"class":3277},[1115,33444,33445,33447,33449,33451],{"class":3270,"line":148},[1115,33446,22684],{"class":3294},[1115,33448,1151],{"class":3277},[1115,33450,33370],{"class":3280},[1115,33452,3283],{"class":3277},[3261,33454,33457],{"className":33455,"code":33456,"language":4279,"meta":3265},[4277],"    One Sample t-test\n\ndata:  x3\nt = -2.4922, df = 9, p-value = 0.0343\nalternative hypothesis: true mean is not equal to 4\n95 percent confidence interval:\n 3.732925 3.987075\nsample estimates:\nmean of x \n     3.86 \n\n    Shapiro-Wilk normality test\n\ndata:  x3\nW = 0.93156, p-value = 0.4634\n",[1434,33458,33456],{"__ignoreMap":3265},[1110,33460,33461,33484,33485,33508],{},[1115,33462,33464],{"className":33463},[1136],[1138,33465,33466],{"xmlns":1140},[1142,33467,33468,33481],{},[1145,33469,33470,33472,33474,33477,33479],{},[1156,33471,1110],{},[1148,33473,1914],{},[1919,33475,33476],{},"0,0343",[1148,33478,5682],{},[1919,33480,9160],{},[1172,33482,33483],{"encoding":1174},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,33486,33488],{"className":33487},[1136],[1138,33489,33490],{"xmlns":1140},[1142,33491,33492,33505],{},[1145,33493,33494,33496,33498,33501,33503],{},[1156,33495,1110],{},[1148,33497,1914],{},[1919,33499,33500],{},"0,4634",[1148,33502,5755],{},[1919,33504,9160],{},[1172,33506,33507],{"encoding":1174},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1437,33510,33512],{"id":33511},"párový-t-test","Párový t-test",[1110,33514,33515,33516,33546,33547,4560,33581,33619,33620,33633,33634,1204,33652,33672,33673,33690,33691,32235],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,33517,33519],{"className":33518},[1136],[1138,33520,33521],{"xmlns":1140},[1142,33522,33523,33543],{},[1145,33524,33525,33527,33533,33535,33541],{},[1148,33526,1151],{"stretchy":1150},[1217,33528,33529,33531],{},[1156,33530,2168],{},[1156,33532,1223],{},[1148,33534,1164],{"separator":1121},[1217,33536,33537,33539],{},[1156,33538,12233],{},[1156,33540,1223],{},[1148,33542,1170],{"stretchy":1150},[1172,33544,33545],{"encoding":1174},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,33548,33550],{"className":33549},[1136],[1138,33551,33552],{"xmlns":1140},[1142,33553,33554,33578],{},[1145,33555,33556,33562,33564,33570,33572],{},[1217,33557,33558,33560],{},[1156,33559,13297],{},[1156,33561,1223],{},[1148,33563,1914],{},[1217,33565,33566,33568],{},[1156,33567,2168],{},[1156,33569,1223],{},[1148,33571,1990],{},[1217,33573,33574,33576],{},[1156,33575,12233],{},[1156,33577,1223],{},[1172,33579,33580],{"encoding":1174},"D_i = X_i - Y_i",[1115,33582,33584],{"className":33583},[1136],[1138,33585,33586],{"xmlns":1140},[1142,33587,33588,33616],{},[1145,33589,33590,33592,33594,33596,33598,33604,33606,33614],{},[1156,33591,13297],{},[1148,33593,14325],{},[1156,33595,12034],{},[1148,33597,1151],{"stretchy":1150},[1217,33599,33600,33602],{},[1156,33601,1677],{},[1156,33603,13297],{},[1148,33605,1164],{"separator":1121},[8555,33607,33608,33610,33612],{},[1156,33609,1693],{},[1156,33611,13297],{},[1919,33613,2302],{},[1148,33615,1170],{"stretchy":1150},[1172,33617,33618],{"encoding":1174},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,33621,33623],{"className":33622},[1136],[1138,33624,33625],{"xmlns":1140},[1142,33626,33627,33631],{},[1145,33628,33629],{},[1156,33630,1292],{},[1172,33632,1292],{"encoding":1174}," dvojic se určí ",[1115,33635,33637],{"className":33636},[1136],[1138,33638,33639],{"xmlns":1140},[1142,33640,33641,33649],{},[1145,33642,33643],{},[1153,33644,33645,33647],{"accent":1121},[1156,33646,12940],{},[1148,33648,1161],{},[1172,33650,33651],{"encoding":1174},"\\bar{d}",[1115,33653,33655],{"className":33654},[1136],[1138,33656,33657],{"xmlns":1140},[1142,33658,33659,33669],{},[1145,33660,33661],{},[8555,33662,33663,33665,33667],{},[1156,33664,1198],{},[1156,33666,12940],{},[1919,33668,2302],{},[1172,33670,33671],{"encoding":1174},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,33674,33676],{"className":33675},[1136],[1138,33677,33678],{"xmlns":1140},[1142,33679,33680,33688],{},[1145,33681,33682],{},[1217,33683,33684,33686],{},[1156,33685,1677],{},[1919,33687,2780],{},[1172,33689,32220],{"encoding":1174}," (obvykle 0) a ",[1115,33692,33694],{"className":33693},[1136],[1138,33695,33696],{"xmlns":1140},[1142,33697,33698,33706],{},[1145,33699,33700],{},[1217,33701,33702,33704],{},[1156,33703,1677],{},[1156,33705,13297],{},[1172,33707,33708],{"encoding":1174},"\\mu_D",[1115,33710,33712],{"className":33711},[1136],[1138,33713,33714],{"xmlns":1140,"display":1897},[1142,33715,33716,33766],{},[1145,33717,33718,33720,33722,33746,33750,33752,33764],{},[1156,33719,5427],{},[1148,33721,1914],{},[1916,33723,33724,33740],{},[1145,33725,33726,33732,33734],{},[1153,33727,33728,33730],{"accent":1121},[1156,33729,12940],{},[1148,33731,1161],{},[1148,33733,1990],{},[1217,33735,33736,33738],{},[1156,33737,1677],{},[1919,33739,2780],{},[1217,33741,33742,33744],{},[1156,33743,1198],{},[1156,33745,12940],{},[5460,33747,33748],{},[1156,33749,1292],{},[1148,33751,14325],{},[1217,33753,33754,33756],{},[1156,33755,12288],{},[1145,33757,33758,33760,33762],{},[1156,33759,1292],{},[1148,33761,1990],{},[1919,33763,1921],{},[1156,33765,1247],{"mathvariant":2014},[1172,33767,33768],{"encoding":1174},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1459,33770,33771,33828],{},[1462,33772,33773],{},[1465,33774,33775,33794,33813],{},[1468,33776,33777],{},[1115,33778,33780],{"className":33779},[1136],[1138,33781,33782],{"xmlns":1140},[1142,33783,33784,33792],{},[1145,33785,33786],{},[1217,33787,33788,33790],{},[1156,33789,6797],{},[1919,33791,2780],{},[1172,33793,6802],{"encoding":1174},[1468,33795,33796],{},[1115,33797,33799],{"className":33798},[1136],[1138,33800,33801],{"xmlns":1140},[1142,33802,33803,33811],{},[1145,33804,33805],{},[1217,33806,33807,33809],{},[1156,33808,6797],{},[1919,33810,1921],{},[1172,33812,8200],{"encoding":1174},[1468,33814,32358,33815],{},[1115,33816,33818],{"className":33817},[1136],[1138,33819,33820],{"xmlns":1140},[1142,33821,33822,33826],{},[1145,33823,33824],{},[1156,33825,6835],{},[1172,33827,6835],{"encoding":1174},[1477,33829,33830,33927,34032],{},[1465,33831,33832,33860,33888],{},[1482,33833,33834],{},[1115,33835,33837],{"className":33836},[1136],[1138,33838,33839],{"xmlns":1140},[1142,33840,33841,33857],{},[1145,33842,33843,33849,33851],{},[1217,33844,33845,33847],{},[1156,33846,1677],{},[1156,33848,13297],{},[1148,33850,11884],{},[1217,33852,33853,33855],{},[1156,33854,1677],{},[1919,33856,2780],{},[1172,33858,33859],{"encoding":1174},"\\mu_D \\le \\mu_0",[1482,33861,33862],{},[1115,33863,33865],{"className":33864},[1136],[1138,33866,33867],{"xmlns":1140},[1142,33868,33869,33885],{},[1145,33870,33871,33877,33879],{},[1217,33872,33873,33875],{},[1156,33874,1677],{},[1156,33876,13297],{},[1148,33878,5755],{},[1217,33880,33881,33883],{},[1156,33882,1677],{},[1919,33884,2780],{},[1172,33886,33887],{"encoding":1174},"\\mu_D > \\mu_0",[1482,33889,33890],{},[1115,33891,33893],{"className":33892},[1136],[1138,33894,33895],{"xmlns":1140},[1142,33896,33897,33925],{},[1145,33898,33899,33901,33903,33915,33917,33919,33921,33923],{},[1156,33900,12288],{},[1148,33902,8553],{},[1217,33904,33905,33907],{},[1156,33906,12288],{},[1145,33908,33909,33911,33913],{},[1919,33910,1921],{},[1148,33912,1990],{},[1156,33914,8567],{},[1148,33916,1151],{"stretchy":1150},[1156,33918,1292],{},[1148,33920,1990],{},[1919,33922,1921],{},[1148,33924,1170],{"stretchy":1150},[1172,33926,32463],{"encoding":1174},[1465,33928,33929,33957,33985],{},[1482,33930,33931],{},[1115,33932,33934],{"className":33933},[1136],[1138,33935,33936],{"xmlns":1140},[1142,33937,33938,33954],{},[1145,33939,33940,33946,33948],{},[1217,33941,33942,33944],{},[1156,33943,1677],{},[1156,33945,13297],{},[1148,33947,1914],{},[1217,33949,33950,33952],{},[1156,33951,1677],{},[1919,33953,2780],{},[1172,33955,33956],{"encoding":1174},"\\mu_D = \\mu_0",[1482,33958,33959],{},[1115,33960,33962],{"className":33961},[1136],[1138,33963,33964],{"xmlns":1140},[1142,33965,33966,33982],{},[1145,33967,33968,33974,33976],{},[1217,33969,33970,33972],{},[1156,33971,1677],{},[1156,33973,13297],{},[1148,33975,16087],{"mathvariant":2014},[1217,33977,33978,33980],{},[1156,33979,1677],{},[1919,33981,2780],{},[1172,33983,33984],{"encoding":1174},"\\mu_D \\neq \\mu_0",[1482,33986,33987],{},[1115,33988,33990],{"className":33989},[1136],[1138,33991,33992],{"xmlns":1140},[1142,33993,33994,34030],{},[1145,33995,33996,33998,34000,34002,34004,34020,34022,34024,34026,34028],{},[1148,33997,3636],{"stretchy":1150},[1156,33999,12288],{},[1148,34001,3636],{"stretchy":1150},[1148,34003,8553],{},[1217,34005,34006,34008],{},[1156,34007,12288],{},[1145,34009,34010,34012,34014,34016,34018],{},[1919,34011,1921],{},[1148,34013,1990],{},[1156,34015,8567],{},[1156,34017,4412],{"mathvariant":2014},[1919,34019,2302],{},[1148,34021,1151],{"stretchy":1150},[1156,34023,1292],{},[1148,34025,1990],{},[1919,34027,1921],{},[1148,34029,1170],{"stretchy":1150},[1172,34031,32561],{"encoding":1174},[1465,34033,34034,34062,34090],{},[1482,34035,34036],{},[1115,34037,34039],{"className":34038},[1136],[1138,34040,34041],{"xmlns":1140},[1142,34042,34043,34059],{},[1145,34044,34045,34051,34053],{},[1217,34046,34047,34049],{},[1156,34048,1677],{},[1156,34050,13297],{},[1148,34052,8553],{},[1217,34054,34055,34057],{},[1156,34056,1677],{},[1919,34058,2780],{},[1172,34060,34061],{"encoding":1174},"\\mu_D \\ge \\mu_0",[1482,34063,34064],{},[1115,34065,34067],{"className":34066},[1136],[1138,34068,34069],{"xmlns":1140},[1142,34070,34071,34087],{},[1145,34072,34073,34079,34081],{},[1217,34074,34075,34077],{},[1156,34076,1677],{},[1156,34078,13297],{},[1148,34080,5682],{},[1217,34082,34083,34085],{},[1156,34084,1677],{},[1919,34086,2780],{},[1172,34088,34089],{"encoding":1174},"\\mu_D \u003C \\mu_0",[1482,34091,34092],{},[1115,34093,34095],{"className":34094},[1136],[1138,34096,34097],{"xmlns":1140},[1142,34098,34099,34129],{},[1145,34100,34101,34103,34105,34107,34119,34121,34123,34125,34127],{},[1156,34102,12288],{},[1148,34104,11884],{},[1148,34106,1990],{},[1217,34108,34109,34111],{},[1156,34110,12288],{},[1145,34112,34113,34115,34117],{},[1919,34114,1921],{},[1148,34116,1990],{},[1156,34118,8567],{},[1148,34120,1151],{"stretchy":1150},[1156,34122,1292],{},[1148,34124,1990],{},[1919,34126,1921],{},[1148,34128,1170],{"stretchy":1150},[1172,34130,32653],{"encoding":1174},[1103,34132,34134,34141,34283,34347,34433],{"className":34133,"dataCallout":2145},[1106,2144],[1110,34135,34137,34140],{"className":34136},[1113],[1115,34138],{"className":34139,"ariaHidden":1121},[1118,2152,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,34142,34143,34144,34162,34163,34181,34182,34200,34201,34234,34235,34258,34259,34282],{},"U ",[1115,34145,34147],{"className":34146},[1136],[1138,34148,34149],{"xmlns":1140},[1142,34150,34151,34159],{},[1145,34152,34153,34155,34157],{},[1156,34154,1292],{},[1148,34156,1914],{},[1919,34158,14175],{},[1172,34160,34161],{"encoding":1174},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,34164,34166],{"className":34165},[1136],[1138,34167,34168],{"xmlns":1140},[1142,34169,34170,34178],{},[1145,34171,34172],{},[1217,34173,34174,34176],{},[1156,34175,2168],{},[1156,34177,1223],{},[1172,34179,34180],{"encoding":1174},"X_i",") a po něm (",[1115,34183,34185],{"className":34184},[1136],[1138,34186,34187],{"xmlns":1140},[1142,34188,34189,34197],{},[1145,34190,34191],{},[1217,34192,34193,34195],{},[1156,34194,12233],{},[1156,34196,1223],{},[1172,34198,34199],{"encoding":1174},"Y_i","), diference ",[1115,34202,34204],{"className":34203},[1136],[1138,34205,34206],{"xmlns":1140},[1142,34207,34208,34232],{},[1145,34209,34210,34216,34218,34224,34226],{},[1217,34211,34212,34214],{},[1156,34213,13297],{},[1156,34215,1223],{},[1148,34217,1914],{},[1217,34219,34220,34222],{},[1156,34221,2168],{},[1156,34223,1223],{},[1148,34225,1990],{},[1217,34227,34228,34230],{},[1156,34229,12233],{},[1156,34231,1223],{},[1172,34233,33580],{"encoding":1174}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,34236,34238],{"className":34237},[1136],[1138,34239,34240],{"xmlns":1140},[1142,34241,34242,34255],{},[1145,34243,34244,34250,34252],{},[1153,34245,34246,34248],{"accent":1121},[1156,34247,12940],{},[1148,34249,1161],{},[1148,34251,1914],{},[1919,34253,34254],{},"0,4",[1172,34256,34257],{"encoding":1174},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,34260,34262],{"className":34261},[1136],[1138,34263,34264],{"xmlns":1140},[1142,34265,34266,34279],{},[1145,34267,34268,34274,34276],{},[1217,34269,34270,34272],{},[1156,34271,1198],{},[1156,34273,12940],{},[1148,34275,1914],{},[1919,34277,34278],{},"0,35",[1172,34280,34281],{"encoding":1174},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,34284,34285,34315,34316,34346],{},[1115,34286,34288],{"className":34287},[1136],[1138,34289,34290],{"xmlns":1140},[1142,34291,34292,34312],{},[1145,34293,34294,34300,34302,34308,34310],{},[1217,34295,34296,34298],{},[1156,34297,6797],{},[1919,34299,2780],{},[1148,34301,2529],{},[1217,34303,34304,34306],{},[1156,34305,1677],{},[1156,34307,13297],{},[1148,34309,11884],{},[1919,34311,2780],{},[1172,34313,34314],{"encoding":1174},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,34317,34319],{"className":34318},[1136],[1138,34320,34321],{"xmlns":1140},[1142,34322,34323,34343],{},[1145,34324,34325,34331,34333,34339,34341],{},[1217,34326,34327,34329],{},[1156,34328,6797],{},[1919,34330,1921],{},[1148,34332,2529],{},[1217,34334,34335,34337],{},[1156,34336,1677],{},[1156,34338,13297],{},[1148,34340,5755],{},[1919,34342,2780],{},[1172,34344,34345],{"encoding":1174},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,34348,34349],{},[1115,34350,34352],{"className":34351},[1136],[1138,34353,34354],{"xmlns":1140},[1142,34355,34356,34430],{},[1145,34357,34358,34360,34362,34374,34378,34380,34383,34385,34387,34389,34391,34393,34395,34397,34409,34411,34413,34415,34417,34419,34421,34423,34425,34428],{},[1156,34359,12288],{},[1148,34361,1914],{},[1916,34363,34364,34372],{},[1145,34365,34366,34368,34370],{},[1919,34367,34254],{},[1148,34369,1990],{},[1919,34371,2780],{},[1919,34373,34278],{},[5460,34375,34376],{},[1919,34377,14175],{},[1148,34379,1914],{},[1919,34381,34382],{},"3,614",[1148,34384,1164],{"separator":1121},[1954,34386],{"width":1956},[1156,34388,6835],{},[1148,34390,1914],{},[1148,34392,8536],{"stretchy":1150},[1156,34394,12288],{},[1148,34396,8553],{},[1217,34398,34399,34401],{},[1156,34400,12288],{},[1145,34402,34403,34405,34407],{},[1919,34404,2780],{},[1148,34406,1164],{"separator":1121},[1919,34408,2378],{},[1148,34410,1151],{"stretchy":1150},[1919,34412,8789],{},[1148,34414,1170],{"stretchy":1150},[1148,34416,8596],{"stretchy":1150},[1148,34418,1914],{},[1148,34420,8536],{"stretchy":1150},[1156,34422,12288],{},[1148,34424,8553],{},[1919,34426,34427],{},"1,833",[1148,34429,8596],{"stretchy":1150},[1172,34431,34432],{"encoding":1174},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,34434,33044,34435,11165,34452,34469],{},[1115,34436,34438],{"className":34437},[1136],[1138,34439,34440],{"xmlns":1140},[1142,34441,34442,34450],{},[1145,34443,34444,34446,34448],{},[1156,34445,12288],{},[1148,34447,12164],{},[1156,34449,6835],{},[1172,34451,33062],{"encoding":1174},[1115,34453,34455],{"className":34454},[1136],[1138,34456,34457],{"xmlns":1140},[1142,34458,34459,34467],{},[1145,34460,34461],{},[1217,34462,34463,34465],{},[1156,34464,6797],{},[1919,34466,2780],{},[1172,34468,6802],{"encoding":1174},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3261,34471,34473],{"className":3263,"code":34472,"language":71,"meta":3265,"style":3265},"dbar \u003C- 0.4; sd_d \u003C- 0.35; n \u003C- 10\nt \u003C- (dbar - 0) \u002F sd_d * sqrt(n)\nt_krit \u003C- qt(0.95, df = n - 1)\nt\nt_krit\n",[1434,34474,34475,34504,34535,34561,34565],{"__ignoreMap":3265},[1115,34476,34477,34480,34482,34485,34487,34490,34492,34495,34497,34499,34501],{"class":3270,"line":10},[1115,34478,34479],{"class":3280},"dbar",[1115,34481,3291],{"class":3273},[1115,34483,34484],{"class":3312}," 0.4",[1115,34486,5832],{"class":3277},[1115,34488,34489],{"class":3280},"sd_d",[1115,34491,3291],{"class":3273},[1115,34493,34494],{"class":3312}," 0.35",[1115,34496,5832],{"class":3277},[1115,34498,1292],{"class":3280},[1115,34500,3291],{"class":3273},[1115,34502,34503],{"class":3312}," 10\n",[1115,34505,34506,34508,34510,34512,34514,34516,34518,34520,34522,34525,34527,34529,34531,34533],{"class":3270,"line":27},[1115,34507,12288],{"class":3280},[1115,34509,3291],{"class":3273},[1115,34511,6173],{"class":3277},[1115,34513,34479],{"class":3280},[1115,34515,6178],{"class":3273},[1115,34517,4166],{"class":3312},[1115,34519,6207],{"class":3277},[1115,34521,4412],{"class":3273},[1115,34523,34524],{"class":3280}," sd_d",[1115,34526,6216],{"class":3273},[1115,34528,6158],{"class":3294},[1115,34530,1151],{"class":3277},[1115,34532,1292],{"class":3280},[1115,34534,3283],{"class":3277},[1115,34536,34537,34539,34541,34543,34545,34547,34549,34551,34553,34555,34557,34559],{"class":3270,"line":148},[1115,34538,33169],{"class":3280},[1115,34540,3291],{"class":3273},[1115,34542,33174],{"class":3294},[1115,34544,1151],{"class":3277},[1115,34546,15958],{"class":3312},[1115,34548,1164],{"class":3273},[1115,34550,15941],{"class":3280},[1115,34552,3309],{"class":3273},[1115,34554,33188],{"class":3280},[1115,34556,6178],{"class":3273},[1115,34558,3882],{"class":3312},[1115,34560,3283],{"class":3277},[1115,34562,34563],{"class":3270,"line":111},[1115,34564,33199],{"class":3280},[1115,34566,34567],{"class":3270,"line":96},[1115,34568,33204],{"class":3280},[3261,34570,34573],{"className":34571,"code":34572,"language":4279,"meta":3265},[4277],"[1] 3.614032\n[1] 1.833113\n",[1434,34574,34572],{"__ignoreMap":3265},[1103,34576,34578,34585,34588,34733,34739],{"className":34577,"dataCallout":11568},[1106,11567],[1110,34579,34581,34584],{"className":34580},[1113],[1115,34582],{"className":34583,"ariaHidden":1121},[1118,11575,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,34586,34587],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3261,34589,34591],{"className":3263,"code":34590,"language":71,"meta":3265,"style":3265},"estA \u003C- c(3282, 2506, 2812, 5453, 3263, 4571, 3121, 2963)\nestB \u003C- c(3271, 2531, 2799, 5471, 3285, 4557, 3139, 2976)\nt.test(estA, estB, paired = TRUE)\nshapiro.test(estA - estB)\n",[1434,34592,34593,34644,34695,34719],{"__ignoreMap":3265},[1115,34594,34595,34598,34600,34602,34604,34607,34609,34612,34614,34617,34619,34622,34624,34627,34629,34632,34634,34637,34639,34642],{"class":3270,"line":10},[1115,34596,34597],{"class":3280},"estA",[1115,34599,3291],{"class":3273},[1115,34601,4142],{"class":3294},[1115,34603,1151],{"class":3277},[1115,34605,34606],{"class":3312},"3282",[1115,34608,1164],{"class":3273},[1115,34610,34611],{"class":3312}," 2506",[1115,34613,1164],{"class":3273},[1115,34615,34616],{"class":3312}," 2812",[1115,34618,1164],{"class":3273},[1115,34620,34621],{"class":3312}," 5453",[1115,34623,1164],{"class":3273},[1115,34625,34626],{"class":3312}," 3263",[1115,34628,1164],{"class":3273},[1115,34630,34631],{"class":3312}," 4571",[1115,34633,1164],{"class":3273},[1115,34635,34636],{"class":3312}," 3121",[1115,34638,1164],{"class":3273},[1115,34640,34641],{"class":3312}," 2963",[1115,34643,3283],{"class":3277},[1115,34645,34646,34649,34651,34653,34655,34658,34660,34663,34665,34668,34670,34673,34675,34678,34680,34683,34685,34688,34690,34693],{"class":3270,"line":27},[1115,34647,34648],{"class":3280},"estB",[1115,34650,3291],{"class":3273},[1115,34652,4142],{"class":3294},[1115,34654,1151],{"class":3277},[1115,34656,34657],{"class":3312},"3271",[1115,34659,1164],{"class":3273},[1115,34661,34662],{"class":3312}," 2531",[1115,34664,1164],{"class":3273},[1115,34666,34667],{"class":3312}," 2799",[1115,34669,1164],{"class":3273},[1115,34671,34672],{"class":3312}," 5471",[1115,34674,1164],{"class":3273},[1115,34676,34677],{"class":3312}," 3285",[1115,34679,1164],{"class":3273},[1115,34681,34682],{"class":3312}," 4557",[1115,34684,1164],{"class":3273},[1115,34686,34687],{"class":3312}," 3139",[1115,34689,1164],{"class":3273},[1115,34691,34692],{"class":3312}," 2976",[1115,34694,3283],{"class":3277},[1115,34696,34697,34699,34701,34703,34705,34708,34710,34713,34715,34717],{"class":3270,"line":148},[1115,34698,32724],{"class":3294},[1115,34700,1151],{"class":3277},[1115,34702,34597],{"class":3280},[1115,34704,1164],{"class":3273},[1115,34706,34707],{"class":3280}," estB",[1115,34709,1164],{"class":3273},[1115,34711,34712],{"class":3280}," paired",[1115,34714,3309],{"class":3273},[1115,34716,3313],{"class":3312},[1115,34718,3283],{"class":3277},[1115,34720,34721,34723,34725,34727,34729,34731],{"class":3270,"line":111},[1115,34722,22684],{"class":3294},[1115,34724,1151],{"class":3277},[1115,34726,34597],{"class":3280},[1115,34728,6178],{"class":3273},[1115,34730,34707],{"class":3280},[1115,34732,3283],{"class":3277},[3261,34734,34737],{"className":34735,"code":34736,"language":4279,"meta":3265},[4277],"    Paired t-test\n\ndata:  estA and estB\nt = -1.2157, df = 7, p-value = 0.2635\nalternative hypothesis: true mean difference is not equal to 0\n95 percent confidence interval:\n -21.351272   6.851272\nsample estimates:\nmean difference \n          -7.25 \n\n    Shapiro-Wilk normality test\n\ndata:  estA - estB\nW = 0.80456, p-value = 0.03203\n",[1434,34738,34736],{"__ignoreMap":3265},[1110,34740,34741,34742,6173,34759,34778,34779,34802],{},"Párový t-test sám nezamítá ",[1115,34743,34745],{"className":34744},[1136],[1138,34746,34747],{"xmlns":1140},[1142,34748,34749,34757],{},[1145,34750,34751],{},[1217,34752,34753,34755],{},[1156,34754,6797],{},[1919,34756,2780],{},[1172,34758,6802],{"encoding":1174},[1115,34760,34762],{"className":34761},[1136],[1138,34763,34764],{"xmlns":1140},[1142,34765,34766,34775],{},[1145,34767,34768,34770,34772],{},[1156,34769,1110],{},[1148,34771,1914],{},[1919,34773,34774],{},"0,2635",[1172,34776,34777],{"encoding":1174},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,34780,34782],{"className":34781},[1136],[1138,34783,34784],{"xmlns":1140},[1142,34785,34786,34799],{},[1145,34787,34788,34790,34792,34795,34797],{},[1156,34789,1110],{},[1148,34791,1914],{},[1919,34793,34794],{},"0,03203",[1148,34796,5682],{},[1919,34798,9160],{},[1172,34800,34801],{"encoding":1174},"p = 0{,}03203 \u003C 0{,}05"," — předpoklad normality diferencí je porušen a výsledek t-testu proto není spolehlivý. Správný postup je ověřit normalitu diferencí dříve, než se párový t-test interpretuje, a při jejím porušení použít párový Wilcoxonův test (viz oddíl Neparametrické testy níže).",[1437,34804,34806],{"id":34805},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,34808,34809,34810,34836,34837,34875,34876,1204,34894,34875,34932,34950,34951,1204,34983,35015,35016,35042,35043,1247],{},"Uvažují se dva nezávislé základní soubory ",[1115,34811,34813],{"className":34812},[1136],[1138,34814,34815],{"xmlns":1140},[1142,34816,34817,34833],{},[1145,34818,34819,34825,34827],{},[1217,34820,34821,34823],{},[1156,34822,14067],{},[1919,34824,1921],{},[1148,34826,1164],{"separator":1121},[1217,34828,34829,34831],{},[1156,34830,14067],{},[1919,34832,2302],{},[1172,34834,34835],{"encoding":1174},"Z_1, Z_2"," se znakem ",[1115,34838,34840],{"className":34839},[1136],[1138,34841,34842],{"xmlns":1140},[1142,34843,34844,34872],{},[1145,34845,34846,34848,34850,34852,34854,34860,34862,34870],{},[1156,34847,2168],{},[1148,34849,14325],{},[1156,34851,12034],{},[1148,34853,1151],{"stretchy":1150},[1217,34855,34856,34858],{},[1156,34857,1677],{},[1919,34859,1921],{},[1148,34861,1164],{"separator":1121},[8555,34863,34864,34866,34868],{},[1156,34865,1693],{},[1919,34867,1921],{},[1919,34869,2302],{},[1148,34871,1170],{"stretchy":1150},[1172,34873,34874],{"encoding":1174},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,34877,34879],{"className":34878},[1136],[1138,34880,34881],{"xmlns":1140},[1142,34882,34883,34891],{},[1145,34884,34885],{},[1217,34886,34887,34889],{},[1156,34888,14067],{},[1919,34890,1921],{},[1172,34892,34893],{"encoding":1174},"Z_1",[1115,34895,34897],{"className":34896},[1136],[1138,34898,34899],{"xmlns":1140},[1142,34900,34901,34929],{},[1145,34902,34903,34905,34907,34909,34911,34917,34919,34927],{},[1156,34904,2168],{},[1148,34906,14325],{},[1156,34908,12034],{},[1148,34910,1151],{"stretchy":1150},[1217,34912,34913,34915],{},[1156,34914,1677],{},[1919,34916,2302],{},[1148,34918,1164],{"separator":1121},[8555,34920,34921,34923,34925],{},[1156,34922,1693],{},[1919,34924,2302],{},[1919,34926,2302],{},[1148,34928,1170],{"stretchy":1150},[1172,34930,34931],{"encoding":1174},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,34933,34935],{"className":34934},[1136],[1138,34936,34937],{"xmlns":1140},[1142,34938,34939,34947],{},[1145,34940,34941],{},[1217,34942,34943,34945],{},[1156,34944,14067],{},[1919,34946,2302],{},[1172,34948,34949],{"encoding":1174},"Z_2",". Z výběrů se určí ",[1115,34952,34954],{"className":34953},[1136],[1138,34955,34956],{"xmlns":1140},[1142,34957,34958,34980],{},[1145,34959,34960,34970,34972],{},[1217,34961,34962,34968],{},[1153,34963,34964,34966],{"accent":1121},[1156,34965,1158],{},[1148,34967,1161],{},[1919,34969,1921],{},[1148,34971,1164],{"separator":1121},[8555,34973,34974,34976,34978],{},[1156,34975,1198],{},[1919,34977,1921],{},[1919,34979,2302],{},[1172,34981,34982],{"encoding":1174},"\\bar{x}_1, s_1^2",[1115,34984,34986],{"className":34985},[1136],[1138,34987,34988],{"xmlns":1140},[1142,34989,34990,35012],{},[1145,34991,34992,35002,35004],{},[1217,34993,34994,35000],{},[1153,34995,34996,34998],{"accent":1121},[1156,34997,1158],{},[1148,34999,1161],{},[1919,35001,2302],{},[1148,35003,1164],{"separator":1121},[8555,35005,35006,35008,35010],{},[1156,35007,1198],{},[1919,35009,2302],{},[1919,35011,2302],{},[1172,35013,35014],{"encoding":1174},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,35017,35019],{"className":35018},[1136],[1138,35020,35021],{"xmlns":1140},[1142,35022,35023,35039],{},[1145,35024,35025,35031,35033],{},[1217,35026,35027,35029],{},[1156,35028,1677],{},[1919,35030,1921],{},[1148,35032,1164],{"separator":1121},[1217,35034,35035,35037],{},[1156,35036,1677],{},[1919,35038,2302],{},[1172,35040,35041],{"encoding":1174},"\\mu_1, \\mu_2",", resp. mezi ",[1115,35044,35046],{"className":35045},[1136],[1138,35047,35048],{"xmlns":1140},[1142,35049,35050,35070],{},[1145,35051,35052,35060,35062],{},[8555,35053,35054,35056,35058],{},[1156,35055,1693],{},[1919,35057,1921],{},[1919,35059,2302],{},[1148,35061,1164],{"separator":1121},[8555,35063,35064,35066,35068],{},[1156,35065,1693],{},[1919,35067,2302],{},[1919,35069,2302],{},[1172,35071,35072],{"encoding":1174},"\\sigma_1^2, \\sigma_2^2",[1818,35074,35076],{"id":35075},"f-test-o-rozptylech","F-test o rozptylech",[1110,35078,35079],{},"Statistika",[1115,35081,35083],{"className":35082},[1136],[1138,35084,35085],{"xmlns":1140,"display":1897},[1142,35086,35087,35143],{},[1145,35088,35089,35091,35093,35111,35113],{},[1156,35090,11867],{},[1148,35092,1914],{},[1916,35094,35095,35103],{},[8555,35096,35097,35099,35101],{},[1156,35098,1198],{},[1919,35100,1921],{},[1919,35102,2302],{},[8555,35104,35105,35107,35109],{},[1156,35106,1198],{},[1919,35108,2302],{},[1919,35110,2302],{},[1148,35112,14325],{},[1217,35114,35115,35117],{},[1156,35116,11867],{},[1145,35118,35119,35125,35127,35129,35131,35133,35139,35141],{},[1217,35120,35121,35123],{},[1156,35122,1292],{},[1919,35124,1921],{},[1148,35126,1990],{},[1919,35128,1921],{},[1148,35130,1164],{"separator":1121},[5009,35132,5011],{},[1217,35134,35135,35137],{},[1156,35136,1292],{},[1919,35138,2302],{},[1148,35140,1990],{},[1919,35142,1921],{},[1172,35144,35145],{"encoding":1174},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,35147,35148,35149,1204,35171,32311],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,35150,35152],{"className":35151},[1136],[1138,35153,35154],{"xmlns":1140},[1142,35155,35156,35168],{},[1145,35157,35158,35164,35166],{},[1217,35159,35160,35162],{},[1156,35161,1292],{},[1919,35163,1921],{},[1148,35165,1990],{},[1919,35167,1921],{},[1172,35169,35170],{"encoding":1174},"n_1-1",[1115,35172,35174],{"className":35173},[1136],[1138,35175,35176],{"xmlns":1140},[1142,35177,35178,35190],{},[1145,35179,35180,35186,35188],{},[1217,35181,35182,35184],{},[1156,35183,1292],{},[1919,35185,2302],{},[1148,35187,1990],{},[1919,35189,1921],{},[1172,35191,35192],{"encoding":1174},"n_2-1",[1459,35194,35195,35252],{},[1462,35196,35197],{},[1465,35198,35199,35218,35237],{},[1468,35200,35201],{},[1115,35202,35204],{"className":35203},[1136],[1138,35205,35206],{"xmlns":1140},[1142,35207,35208,35216],{},[1145,35209,35210],{},[1217,35211,35212,35214],{},[1156,35213,6797],{},[1919,35215,2780],{},[1172,35217,6802],{"encoding":1174},[1468,35219,35220],{},[1115,35221,35223],{"className":35222},[1136],[1138,35224,35225],{"xmlns":1140},[1142,35226,35227,35235],{},[1145,35228,35229],{},[1217,35230,35231,35233],{},[1156,35232,6797],{},[1919,35234,1921],{},[1172,35236,8200],{"encoding":1174},[1468,35238,32358,35239],{},[1115,35240,35242],{"className":35241},[1136],[1138,35243,35244],{"xmlns":1140},[1142,35245,35246,35250],{},[1145,35247,35248],{},[1156,35249,6835],{},[1172,35251,6835],{"encoding":1174},[1477,35253,35254,35368,35541],{},[1465,35255,35256,35284,35312],{},[1482,35257,35258],{},[1115,35259,35261],{"className":35260},[1136],[1138,35262,35263],{"xmlns":1140},[1142,35264,35265,35281],{},[1145,35266,35267,35273,35275],{},[1217,35268,35269,35271],{},[1156,35270,1693],{},[1919,35272,1921],{},[1148,35274,11884],{},[1217,35276,35277,35279],{},[1156,35278,1693],{},[1919,35280,2302],{},[1172,35282,35283],{"encoding":1174},"\\sigma_1 \\le \\sigma_2",[1482,35285,35286],{},[1115,35287,35289],{"className":35288},[1136],[1138,35290,35291],{"xmlns":1140},[1142,35292,35293,35309],{},[1145,35294,35295,35301,35303],{},[1217,35296,35297,35299],{},[1156,35298,1693],{},[1919,35300,1921],{},[1148,35302,5755],{},[1217,35304,35305,35307],{},[1156,35306,1693],{},[1919,35308,2302],{},[1172,35310,35311],{"encoding":1174},"\\sigma_1 > \\sigma_2",[1482,35313,35314],{},[1115,35315,35317],{"className":35316},[1136],[1138,35318,35319],{"xmlns":1140},[1142,35320,35321,35365],{},[1145,35322,35323,35325,35327,35339,35341,35347,35349,35351,35353,35359,35361,35363],{},[1156,35324,11867],{},[1148,35326,8553],{},[1217,35328,35329,35331],{},[1156,35330,11867],{},[1145,35332,35333,35335,35337],{},[1919,35334,1921],{},[1148,35336,1990],{},[1156,35338,8567],{},[1148,35340,1151],{"stretchy":1150},[1217,35342,35343,35345],{},[1156,35344,1292],{},[1919,35346,1921],{},[1148,35348,1990],{},[1919,35350,1921],{},[1148,35352,1164],{"separator":1121},[1217,35354,35355,35357],{},[1156,35356,1292],{},[1919,35358,2302],{},[1148,35360,1990],{},[1919,35362,1921],{},[1148,35364,1170],{"stretchy":1150},[1172,35366,35367],{"encoding":1174},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1465,35369,35370,35398,35426],{},[1482,35371,35372],{},[1115,35373,35375],{"className":35374},[1136],[1138,35376,35377],{"xmlns":1140},[1142,35378,35379,35395],{},[1145,35380,35381,35387,35389],{},[1217,35382,35383,35385],{},[1156,35384,1693],{},[1919,35386,1921],{},[1148,35388,1914],{},[1217,35390,35391,35393],{},[1156,35392,1693],{},[1919,35394,2302],{},[1172,35396,35397],{"encoding":1174},"\\sigma_1 = \\sigma_2",[1482,35399,35400],{},[1115,35401,35403],{"className":35402},[1136],[1138,35404,35405],{"xmlns":1140},[1142,35406,35407,35423],{},[1145,35408,35409,35415,35417],{},[1217,35410,35411,35413],{},[1156,35412,1693],{},[1919,35414,1921],{},[1148,35416,16087],{"mathvariant":2014},[1217,35418,35419,35421],{},[1156,35420,1693],{},[1919,35422,2302],{},[1172,35424,35425],{"encoding":1174},"\\sigma_1 \\neq \\sigma_2",[1482,35427,35428,35482,35483],{},[1115,35429,35431],{"className":35430},[1136],[1138,35432,35433],{"xmlns":1140},[1142,35434,35435,35479],{},[1145,35436,35437,35439,35441,35453,35455,35461,35463,35465,35467,35473,35475,35477],{},[1156,35438,11867],{},[1148,35440,11884],{},[1217,35442,35443,35445],{},[1156,35444,11867],{},[1145,35446,35447,35449,35451],{},[1156,35448,8567],{},[1156,35450,4412],{"mathvariant":2014},[1919,35452,2302],{},[1148,35454,1151],{"stretchy":1150},[1217,35456,35457,35459],{},[1156,35458,1292],{},[1919,35460,1921],{},[1148,35462,1990],{},[1919,35464,1921],{},[1148,35466,1164],{"separator":1121},[1217,35468,35469,35471],{},[1156,35470,1292],{},[1919,35472,2302],{},[1148,35474,1990],{},[1919,35476,1921],{},[1148,35478,1170],{"stretchy":1150},[1172,35480,35481],{"encoding":1174},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,35484,35486],{"className":35485},[1136],[1138,35487,35488],{"xmlns":1140},[1142,35489,35490,35538],{},[1145,35491,35492,35494,35496,35512,35514,35520,35522,35524,35526,35532,35534,35536],{},[1156,35493,11867],{},[1148,35495,8553],{},[1217,35497,35498,35500],{},[1156,35499,11867],{},[1145,35501,35502,35504,35506,35508,35510],{},[1919,35503,1921],{},[1148,35505,1990],{},[1156,35507,8567],{},[1156,35509,4412],{"mathvariant":2014},[1919,35511,2302],{},[1148,35513,1151],{"stretchy":1150},[1217,35515,35516,35518],{},[1156,35517,1292],{},[1919,35519,1921],{},[1148,35521,1990],{},[1919,35523,1921],{},[1148,35525,1164],{"separator":1121},[1217,35527,35528,35530],{},[1156,35529,1292],{},[1919,35531,2302],{},[1148,35533,1990],{},[1919,35535,1921],{},[1148,35537,1170],{"stretchy":1150},[1172,35539,35540],{"encoding":1174},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1465,35542,35543,35571,35599],{},[1482,35544,35545],{},[1115,35546,35548],{"className":35547},[1136],[1138,35549,35550],{"xmlns":1140},[1142,35551,35552,35568],{},[1145,35553,35554,35560,35562],{},[1217,35555,35556,35558],{},[1156,35557,1693],{},[1919,35559,1921],{},[1148,35561,8553],{},[1217,35563,35564,35566],{},[1156,35565,1693],{},[1919,35567,2302],{},[1172,35569,35570],{"encoding":1174},"\\sigma_1 \\ge \\sigma_2",[1482,35572,35573],{},[1115,35574,35576],{"className":35575},[1136],[1138,35577,35578],{"xmlns":1140},[1142,35579,35580,35596],{},[1145,35581,35582,35588,35590],{},[1217,35583,35584,35586],{},[1156,35585,1693],{},[1919,35587,1921],{},[1148,35589,5682],{},[1217,35591,35592,35594],{},[1156,35593,1693],{},[1919,35595,2302],{},[1172,35597,35598],{"encoding":1174},"\\sigma_1 \u003C \\sigma_2",[1482,35600,35601],{},[1115,35602,35604],{"className":35603},[1136],[1138,35605,35606],{"xmlns":1140},[1142,35607,35608,35646],{},[1145,35609,35610,35612,35614,35620,35622,35628,35630,35632,35634,35640,35642,35644],{},[1156,35611,11867],{},[1148,35613,11884],{},[1217,35615,35616,35618],{},[1156,35617,11867],{},[1156,35619,8567],{},[1148,35621,1151],{"stretchy":1150},[1217,35623,35624,35626],{},[1156,35625,1292],{},[1919,35627,1921],{},[1148,35629,1990],{},[1919,35631,1921],{},[1148,35633,1164],{"separator":1121},[1217,35635,35636,35638],{},[1156,35637,1292],{},[1919,35639,2302],{},[1148,35641,1990],{},[1919,35643,1921],{},[1148,35645,1170],{"stretchy":1150},[1172,35647,35648],{"encoding":1174},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[1818,35650,35652],{"id":35651},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,35654,35655],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,35657,35659],{"className":35658},[1136],[1138,35660,35661],{"xmlns":1140,"display":1897},[1142,35662,35663,35840],{},[1145,35664,35665,35671,35673,35749,35797,35799,35801,35810,35812,35818,35820,35826,35828,35834,35836,35838],{},[1217,35666,35667,35669],{},[1156,35668,5427],{},[1919,35670,1921],{},[1148,35672,1914],{},[1916,35674,35675,35699],{},[1145,35676,35677,35687,35689],{},[1217,35678,35679,35685],{},[1153,35680,35681,35683],{"accent":1121},[1156,35682,1158],{},[1148,35684,1161],{},[1919,35686,1921],{},[1148,35688,1990],{},[1217,35690,35691,35697],{},[1153,35692,35693,35695],{"accent":1121},[1156,35694,1158],{},[1148,35696,1161],{},[1919,35698,2302],{},[5460,35700,35701],{},[1145,35702,35703,35705,35711,35713,35715,35717,35725,35727,35729,35735,35737,35739,35741],{},[1148,35704,1151],{"stretchy":1150},[1217,35706,35707,35709],{},[1156,35708,1292],{},[1919,35710,1921],{},[1148,35712,1990],{},[1919,35714,1921],{},[1148,35716,1170],{"stretchy":1150},[8555,35718,35719,35721,35723],{},[1156,35720,1198],{},[1919,35722,1921],{},[1919,35724,2302],{},[1148,35726,5066],{},[1148,35728,1151],{"stretchy":1150},[1217,35730,35731,35733],{},[1156,35732,1292],{},[1919,35734,2302],{},[1148,35736,1990],{},[1919,35738,1921],{},[1148,35740,1170],{"stretchy":1150},[8555,35742,35743,35745,35747],{},[1156,35744,1198],{},[1919,35746,2302],{},[1919,35748,2302],{},[5460,35750,35751],{},[1916,35752,35753,35773],{},[1145,35754,35755,35761,35763,35769,35771],{},[1217,35756,35757,35759],{},[1156,35758,1292],{},[1919,35760,1921],{},[1148,35762,5066],{},[1217,35764,35765,35767],{},[1156,35766,1292],{},[1919,35768,2302],{},[1148,35770,1990],{},[1919,35772,2302],{},[1145,35774,35775,35785,35787],{},[1916,35776,35777,35779],{},[1919,35778,1921],{},[1217,35780,35781,35783],{},[1156,35782,1292],{},[1919,35784,1921],{},[1148,35786,5066],{},[1916,35788,35789,35791],{},[1919,35790,1921],{},[1217,35792,35793,35795],{},[1156,35794,1292],{},[1919,35796,2302],{},[1148,35798,1164],{"separator":1121},[1954,35800],{"width":1956},[8555,35802,35803,35805,35807],{},[1156,35804,12288],{},[1156,35806,1110],{},[1148,35808,35809],{},"∗",[1148,35811,1914],{},[1217,35813,35814,35816],{},[1156,35815,12288],{},[1156,35817,1110],{},[1148,35819,1151],{"stretchy":1150},[1217,35821,35822,35824],{},[1156,35823,1292],{},[1919,35825,1921],{},[1148,35827,5066],{},[1217,35829,35830,35832],{},[1156,35831,1292],{},[1919,35833,2302],{},[1148,35835,1990],{},[1919,35837,2302],{},[1148,35839,1170],{"stretchy":1150},[1172,35841,35842],{"encoding":1174},"T_1 = \\frac{\\bar{x}_1 - \\bar{x}_2}{\\sqrt{(n_1-1)s_1^2 + (n_2-1)s_2^2}}\\sqrt{\\frac{n_1+n_2-2}{\\frac1{n_1}+\\frac1{n_2}}}, \\qquad t_p^* = t_p(n_1+n_2-2)",[1110,35844,35845,35846,35875],{},"se použije, pokud jsou rozptyly ",[1115,35847,35849],{"className":35848},[1136],[1138,35850,35851],{"xmlns":1140},[1142,35852,35853,35873],{},[1145,35854,35855,35863,35865],{},[8555,35856,35857,35859,35861],{},[1156,35858,1693],{},[1919,35860,1921],{},[1919,35862,2302],{},[1148,35864,1164],{"separator":1121},[8555,35866,35867,35869,35871],{},[1156,35868,1693],{},[1919,35870,2302],{},[1919,35872,2302],{},[1172,35874,35072],{"encoding":1174}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,35877,35879],{"className":35878},[1136],[1138,35880,35881],{"xmlns":1140,"display":1897},[1142,35882,35883,36095],{},[1145,35884,35885,35891,35893,35957,35959,35961,35969,35971,36093],{},[1217,35886,35887,35889],{},[1156,35888,5427],{},[1919,35890,2302],{},[1148,35892,1914],{},[1916,35894,35895,35919],{},[1145,35896,35897,35907,35909],{},[1217,35898,35899,35905],{},[1153,35900,35901,35903],{"accent":1121},[1156,35902,1158],{},[1148,35904,1161],{},[1919,35906,1921],{},[1148,35908,1990],{},[1217,35910,35911,35917],{},[1153,35912,35913,35915],{"accent":1121},[1156,35914,1158],{},[1148,35916,1161],{},[1919,35918,2302],{},[5460,35920,35921],{},[1145,35922,35923,35931,35933,35939,35941,35949,35951],{},[8555,35924,35925,35927,35929],{},[1156,35926,1198],{},[1919,35928,1921],{},[1919,35930,2302],{},[1156,35932,4412],{"mathvariant":2014},[1217,35934,35935,35937],{},[1156,35936,1292],{},[1919,35938,1921],{},[1148,35940,5066],{},[8555,35942,35943,35945,35947],{},[1156,35944,1198],{},[1919,35946,2302],{},[1919,35948,2302],{},[1156,35950,4412],{"mathvariant":2014},[1217,35952,35953,35955],{},[1156,35954,1292],{},[1919,35956,2302],{},[1148,35958,1164],{"separator":1121},[1954,35960],{"width":1956},[8555,35962,35963,35965,35967],{},[1156,35964,12288],{},[1156,35966,1110],{},[1148,35968,35809],{},[1148,35970,1914],{},[1916,35972,35973,36053],{},[1145,35974,35975,35993,35999,36001,36007,36009,36011,36013,36015,36033,36039,36041,36047,36049,36051],{},[4995,35976,35977],{"scriptlevel":2780,"displaystyle":1121},[1916,35978,35979,35987],{},[8555,35980,35981,35983,35985],{},[1156,35982,1198],{},[1919,35984,1921],{},[1919,35986,2302],{},[1217,35988,35989,35991],{},[1156,35990,1292],{},[1919,35992,1921],{},[1217,35994,35995,35997],{},[1156,35996,12288],{},[1156,35998,1110],{},[1148,36000,1151],{"stretchy":1150},[1217,36002,36003,36005],{},[1156,36004,1292],{},[1919,36006,1921],{},[1148,36008,1990],{},[1919,36010,1921],{},[1148,36012,1170],{"stretchy":1150},[1148,36014,5066],{},[4995,36016,36017],{"scriptlevel":2780,"displaystyle":1121},[1916,36018,36019,36027],{},[8555,36020,36021,36023,36025],{},[1156,36022,1198],{},[1919,36024,2302],{},[1919,36026,2302],{},[1217,36028,36029,36031],{},[1156,36030,1292],{},[1919,36032,2302],{},[1217,36034,36035,36037],{},[1156,36036,12288],{},[1156,36038,1110],{},[1148,36040,1151],{"stretchy":1150},[1217,36042,36043,36045],{},[1156,36044,1292],{},[1919,36046,2302],{},[1148,36048,1990],{},[1919,36050,1921],{},[1148,36052,1170],{"stretchy":1150},[1145,36054,36055,36073,36075],{},[4995,36056,36057],{"scriptlevel":2780,"displaystyle":1121},[1916,36058,36059,36067],{},[8555,36060,36061,36063,36065],{},[1156,36062,1198],{},[1919,36064,1921],{},[1919,36066,2302],{},[1217,36068,36069,36071],{},[1156,36070,1292],{},[1919,36072,1921],{},[1148,36074,5066],{},[4995,36076,36077],{"scriptlevel":2780,"displaystyle":1121},[1916,36078,36079,36087],{},[8555,36080,36081,36083,36085],{},[1156,36082,1198],{},[1919,36084,2302],{},[1919,36086,2302],{},[1217,36088,36089,36091],{},[1156,36090,1292],{},[1919,36092,2302],{},[1156,36094,1247],{"mathvariant":2014},[1172,36096,36097],{"encoding":1174},"T_2 = \\frac{\\bar{x}_1-\\bar{x}_2}{\\sqrt{s_1^2\u002Fn_1 + s_2^2\u002Fn_2}}, \\qquad t_p^* = \\frac{\\dfrac{s_1^2}{n_1}t_p(n_1-1) + \\dfrac{s_2^2}{n_2}t_p(n_2-1)}{\\dfrac{s_1^2}{n_1}+\\dfrac{s_2^2}{n_2}}.",[1459,36099,36100,36157],{},[1462,36101,36102],{},[1465,36103,36104,36123,36142],{},[1468,36105,36106],{},[1115,36107,36109],{"className":36108},[1136],[1138,36110,36111],{"xmlns":1140},[1142,36112,36113,36121],{},[1145,36114,36115],{},[1217,36116,36117,36119],{},[1156,36118,6797],{},[1919,36120,2780],{},[1172,36122,6802],{"encoding":1174},[1468,36124,36125],{},[1115,36126,36128],{"className":36127},[1136],[1138,36129,36130],{"xmlns":1140},[1142,36131,36132,36140],{},[1145,36133,36134],{},[1217,36135,36136,36138],{},[1156,36137,6797],{},[1919,36139,1921],{},[1172,36141,8200],{"encoding":1174},[1468,36143,32358,36144],{},[1115,36145,36147],{"className":36146},[1136],[1138,36148,36149],{"xmlns":1140},[1142,36150,36151,36155],{},[1145,36152,36153],{},[1156,36154,6835],{},[1172,36156,6835],{"encoding":1174},[1477,36158,36159,36243,36331],{},[1465,36160,36161,36189,36217],{},[1482,36162,36163],{},[1115,36164,36166],{"className":36165},[1136],[1138,36167,36168],{"xmlns":1140},[1142,36169,36170,36186],{},[1145,36171,36172,36178,36180],{},[1217,36173,36174,36176],{},[1156,36175,1677],{},[1919,36177,1921],{},[1148,36179,11884],{},[1217,36181,36182,36184],{},[1156,36183,1677],{},[1919,36185,2302],{},[1172,36187,36188],{"encoding":1174},"\\mu_1 \\le \\mu_2",[1482,36190,36191],{},[1115,36192,36194],{"className":36193},[1136],[1138,36195,36196],{"xmlns":1140},[1142,36197,36198,36214],{},[1145,36199,36200,36206,36208],{},[1217,36201,36202,36204],{},[1156,36203,1677],{},[1919,36205,1921],{},[1148,36207,5755],{},[1217,36209,36210,36212],{},[1156,36211,1677],{},[1919,36213,2302],{},[1172,36215,36216],{"encoding":1174},"\\mu_1 > \\mu_2",[1482,36218,36219],{},[1115,36220,36222],{"className":36221},[1136],[1138,36223,36224],{"xmlns":1140},[1142,36225,36226,36240],{},[1145,36227,36228,36230,36232],{},[1156,36229,12288],{},[1148,36231,8553],{},[8555,36233,36234,36236,36238],{},[1156,36235,12288],{},[1156,36237,1110],{},[1148,36239,35809],{},[1172,36241,36242],{"encoding":1174},"t \\ge t_p^*",[1465,36244,36245,36273,36301],{},[1482,36246,36247],{},[1115,36248,36250],{"className":36249},[1136],[1138,36251,36252],{"xmlns":1140},[1142,36253,36254,36270],{},[1145,36255,36256,36262,36264],{},[1217,36257,36258,36260],{},[1156,36259,1677],{},[1919,36261,1921],{},[1148,36263,1914],{},[1217,36265,36266,36268],{},[1156,36267,1677],{},[1919,36269,2302],{},[1172,36271,36272],{"encoding":1174},"\\mu_1 = \\mu_2",[1482,36274,36275],{},[1115,36276,36278],{"className":36277},[1136],[1138,36279,36280],{"xmlns":1140},[1142,36281,36282,36298],{},[1145,36283,36284,36290,36292],{},[1217,36285,36286,36288],{},[1156,36287,1677],{},[1919,36289,1921],{},[1148,36291,16087],{"mathvariant":2014},[1217,36293,36294,36296],{},[1156,36295,1677],{},[1919,36297,2302],{},[1172,36299,36300],{"encoding":1174},"\\mu_1 \\neq \\mu_2",[1482,36302,36303],{},[1115,36304,36306],{"className":36305},[1136],[1138,36307,36308],{"xmlns":1140},[1142,36309,36310,36328],{},[1145,36311,36312,36314,36316,36318,36320],{},[1148,36313,3636],{"stretchy":1150},[1156,36315,12288],{},[1148,36317,3636],{"stretchy":1150},[1148,36319,8553],{},[8555,36321,36322,36324,36326],{},[1156,36323,12288],{},[1156,36325,1110],{},[1148,36327,35809],{},[1172,36329,36330],{"encoding":1174},"\\lvert t \\rvert \\ge t_p^*",[1465,36332,36333,36361,36389],{},[1482,36334,36335],{},[1115,36336,36338],{"className":36337},[1136],[1138,36339,36340],{"xmlns":1140},[1142,36341,36342,36358],{},[1145,36343,36344,36350,36352],{},[1217,36345,36346,36348],{},[1156,36347,1677],{},[1919,36349,1921],{},[1148,36351,8553],{},[1217,36353,36354,36356],{},[1156,36355,1677],{},[1919,36357,2302],{},[1172,36359,36360],{"encoding":1174},"\\mu_1 \\ge \\mu_2",[1482,36362,36363],{},[1115,36364,36366],{"className":36365},[1136],[1138,36367,36368],{"xmlns":1140},[1142,36369,36370,36386],{},[1145,36371,36372,36378,36380],{},[1217,36373,36374,36376],{},[1156,36375,1677],{},[1919,36377,1921],{},[1148,36379,5682],{},[1217,36381,36382,36384],{},[1156,36383,1677],{},[1919,36385,2302],{},[1172,36387,36388],{"encoding":1174},"\\mu_1 \u003C \\mu_2",[1482,36390,36391],{},[1115,36392,36394],{"className":36393},[1136],[1138,36395,36396],{"xmlns":1140},[1142,36397,36398,36414],{},[1145,36399,36400,36402,36404,36406],{},[1156,36401,12288],{},[1148,36403,11884],{},[1148,36405,1990],{},[8555,36407,36408,36410,36412],{},[1156,36409,12288],{},[1156,36411,1110],{},[1148,36413,35809],{},[1172,36415,36416],{"encoding":1174},"t \\le -t_p^*",[1110,36418,36419,36420,35482,36438,1247],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,36421,36423],{"className":36422},[1136],[1138,36424,36425],{"xmlns":1140},[1142,36426,36427,36435],{},[1145,36428,36429],{},[1217,36430,36431,36433],{},[1156,36432,5427],{},[1919,36434,1921],{},[1172,36436,36437],{"encoding":1174},"T_1",[1115,36439,36441],{"className":36440},[1136],[1138,36442,36443],{"xmlns":1140},[1142,36444,36445,36453],{},[1145,36446,36447],{},[1217,36448,36449,36451],{},[1156,36450,5427],{},[1919,36452,2302],{},[1172,36454,36455],{"encoding":1174},"T_2",[1110,36457,36458],{},[1527,36459],{"alt":36460,"className":36461,"src":36462},"mask-th-f-kriticky-obor",[1531,1532],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,36464,36466,36473,36623,36704,36833,36871,36944,37083],{"className":36465,"dataCallout":2145},[1106,2144],[1110,36467,36469,36472],{"className":36468},[1113],[1115,36470],{"className":36471,"ariaHidden":1121},[1118,2152,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,36474,36475,36476,1176,36498,36524,36525,36549,36550,1176,36572,36524,36598,36622],{},"Pevnost plastových dílů: dodavatel A (",[1115,36477,36479],{"className":36478},[1136],[1138,36480,36481],{"xmlns":1140},[1142,36482,36483,36495],{},[1145,36484,36485,36491,36493],{},[1217,36486,36487,36489],{},[1156,36488,1292],{},[1919,36490,1921],{},[1148,36492,1914],{},[1919,36494,14175],{},[1172,36496,36497],{"encoding":1174},"n_1 = 10",[1115,36499,36501],{"className":36500},[1136],[1138,36502,36503],{"xmlns":1140},[1142,36504,36505,36521],{},[1145,36506,36507,36517,36519],{},[1217,36508,36509,36515],{},[1153,36510,36511,36513],{"accent":1121},[1156,36512,1158],{},[1148,36514,1161],{},[1919,36516,1921],{},[1148,36518,1914],{},[1919,36520,8822],{},[1172,36522,36523],{"encoding":1174},"\\bar{x}_1 = 82"," MPa, ",[1115,36526,36528],{"className":36527},[1136],[1138,36529,36530],{"xmlns":1140},[1142,36531,36532,36546],{},[1145,36533,36534,36542,36544],{},[8555,36535,36536,36538,36540],{},[1156,36537,1198],{},[1919,36539,1921],{},[1919,36541,2302],{},[1148,36543,1914],{},[1919,36545,9232],{},[1172,36547,36548],{"encoding":1174},"s_1^2 = 25","), dodavatel B (",[1115,36551,36553],{"className":36552},[1136],[1138,36554,36555],{"xmlns":1140},[1142,36556,36557,36569],{},[1145,36558,36559,36565,36567],{},[1217,36560,36561,36563],{},[1156,36562,1292],{},[1919,36564,2302],{},[1148,36566,1914],{},[1919,36568,7485],{},[1172,36570,36571],{"encoding":1174},"n_2 = 12",[1115,36573,36575],{"className":36574},[1136],[1138,36576,36577],{"xmlns":1140},[1142,36578,36579,36595],{},[1145,36580,36581,36591,36593],{},[1217,36582,36583,36589],{},[1153,36584,36585,36587],{"accent":1121},[1156,36586,1158],{},[1148,36588,1161],{},[1919,36590,2302],{},[1148,36592,1914],{},[1919,36594,19846],{},[1172,36596,36597],{"encoding":1174},"\\bar{x}_2 = 75",[1115,36599,36601],{"className":36600},[1136],[1138,36602,36603],{"xmlns":1140},[1142,36604,36605,36619],{},[1145,36606,36607,36615,36617],{},[8555,36608,36609,36611,36613],{},[1156,36610,1198],{},[1919,36612,2302],{},[1919,36614,2302],{},[1148,36616,1914],{},[1919,36618,2614],{},[1172,36620,36621],{"encoding":1174},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,36624,36625,6884,36628,1176,36666,1247],{},[1445,36626,36627],{},"Krok 1 — F-test rozptylů.",[1115,36629,36631],{"className":36630},[1136],[1138,36632,36633],{"xmlns":1140},[1142,36634,36635,36663],{},[1145,36636,36637,36643,36645,36653,36655],{},[1217,36638,36639,36641],{},[1156,36640,6797],{},[1919,36642,2780],{},[1148,36644,2529],{},[8555,36646,36647,36649,36651],{},[1156,36648,1693],{},[1919,36650,1921],{},[1919,36652,2302],{},[1148,36654,1914],{},[8555,36656,36657,36659,36661],{},[1156,36658,1693],{},[1919,36660,2302],{},[1919,36662,2302],{},[1172,36664,36665],{"encoding":1174},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,36667,36669],{"className":36668},[1136],[1138,36670,36671],{"xmlns":1140},[1142,36672,36673,36701],{},[1145,36674,36675,36681,36683,36691,36693],{},[1217,36676,36677,36679],{},[1156,36678,6797],{},[1919,36680,1921],{},[1148,36682,2529],{},[8555,36684,36685,36687,36689],{},[1156,36686,1693],{},[1919,36688,1921],{},[1919,36690,2302],{},[1148,36692,16087],{"mathvariant":2014},[8555,36694,36695,36697,36699],{},[1156,36696,1693],{},[1919,36698,2302],{},[1919,36700,2302],{},[1172,36702,36703],{"encoding":1174},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,36705,36706],{},[1115,36707,36709],{"className":36708},[1136],[1138,36710,36711],{"xmlns":1140},[1142,36712,36713,36830],{},[1145,36714,36715,36717,36719,36725,36727,36730,36732,36734,36736,36738,36740,36742,36744,36757,36759,36761,36763,36765,36767,36770,36773,36775,36777,36779,36792,36794,36796,36798,36800,36802,36804,36806,36808,36810,36812,36815,36817,36819,36821,36823,36825,36828],{},[1156,36716,11867],{},[1148,36718,1914],{},[1916,36720,36721,36723],{},[1919,36722,9232],{},[1919,36724,2614],{},[1148,36726,1914],{},[1919,36728,36729],{},"1,5625",[1148,36731,1164],{"separator":1121},[1954,36733],{"width":1956},[1156,36735,6835],{},[1148,36737,1914],{},[1148,36739,8536],{"stretchy":1150},[1156,36741,11867],{},[1148,36743,11884],{},[1217,36745,36746,36748],{},[1156,36747,11867],{},[1145,36749,36750,36752,36754],{},[1919,36751,2780],{},[1148,36753,1164],{"separator":1121},[1919,36755,36756],{},"025",[1148,36758,1151],{"stretchy":1150},[1919,36760,8789],{},[1148,36762,1164],{"separator":1121},[1919,36764,2644],{},[1148,36766,1170],{"stretchy":1150},[5009,36768,36769],{},"  ",[5009,36771,36772],{},"nebo",[5009,36774,36769],{},[1156,36776,11867],{},[1148,36778,8553],{},[1217,36780,36781,36783],{},[1156,36782,11867],{},[1145,36784,36785,36787,36789],{},[1919,36786,2780],{},[1148,36788,1164],{"separator":1121},[1919,36790,36791],{},"975",[1148,36793,1151],{"stretchy":1150},[1919,36795,8789],{},[1148,36797,1164],{"separator":1121},[1919,36799,2644],{},[1148,36801,1170],{"stretchy":1150},[1148,36803,8596],{"stretchy":1150},[1148,36805,1914],{},[1148,36807,8536],{"stretchy":1150},[1156,36809,11867],{},[1148,36811,11884],{},[1919,36813,36814],{},"0,256",[5009,36816,36769],{},[5009,36818,36772],{},[5009,36820,36769],{},[1156,36822,11867],{},[1148,36824,8553],{},[1919,36826,36827],{},"3,588",[1148,36829,8596],{"stretchy":1150},[1172,36831,36832],{"encoding":1174},"F = \\frac{25}{16} = 1{,}5625, \\qquad W = \\{F \\le F_{0,025}(9,11) \\;\\text{nebo}\\; F \\ge F_{0,975}(9,11)\\} = \\{F \\le 0{,}256 \\;\\text{nebo}\\; F \\ge 3{,}588\\}",[1110,36834,36835,36853,36854,1247],{},[1115,36836,36838],{"className":36837},[1136],[1138,36839,36840],{"xmlns":1140},[1142,36841,36842,36850],{},[1145,36843,36844,36846,36848],{},[1156,36845,11867],{},[1148,36847,31919],{"mathvariant":2014},[1156,36849,6835],{},[1172,36851,36852],{"encoding":1174},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,36855,36857],{"className":36856},[1136],[1138,36858,36859],{"xmlns":1140},[1142,36860,36861,36869],{},[1145,36862,36863],{},[1217,36864,36865,36867],{},[1156,36866,5427],{},[1919,36868,1921],{},[1172,36870,36437],{"encoding":1174},[1110,36872,36873,6884,36876,1176,36910,1247],{},[1445,36874,36875],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,36877,36879],{"className":36878},[1136],[1138,36880,36881],{"xmlns":1140},[1142,36882,36883,36907],{},[1145,36884,36885,36891,36893,36899,36901],{},[1217,36886,36887,36889],{},[1156,36888,6797],{},[1919,36890,2780],{},[1148,36892,2529],{},[1217,36894,36895,36897],{},[1156,36896,1677],{},[1919,36898,1921],{},[1148,36900,1914],{},[1217,36902,36903,36905],{},[1156,36904,1677],{},[1919,36906,2302],{},[1172,36908,36909],{"encoding":1174},"H_0: \\mu_1 = \\mu_2",[1115,36911,36913],{"className":36912},[1136],[1138,36914,36915],{"xmlns":1140},[1142,36916,36917,36941],{},[1145,36918,36919,36925,36927,36933,36935],{},[1217,36920,36921,36923],{},[1156,36922,6797],{},[1919,36924,1921],{},[1148,36926,2529],{},[1217,36928,36929,36931],{},[1156,36930,1677],{},[1919,36932,1921],{},[1148,36934,16087],{"mathvariant":2014},[1217,36936,36937,36939],{},[1156,36938,1677],{},[1919,36940,2302],{},[1172,36942,36943],{"encoding":1174},"H_1: \\mu_1 \\neq \\mu_2",[1110,36945,36946],{},[1115,36947,36949],{"className":36948},[1136],[1138,36950,36951],{"xmlns":1140},[1142,36952,36953,37080],{},[1145,36954,36955,36963,36965,36985,36987,36990,36992,36994,36996,36998,37012,37020,37022,37025,37027,37029,37031,37033,37035,37037,37039,37041,37043,37055,37057,37059,37061,37063,37065,37067,37069,37071,37073,37075,37078],{},[8555,36956,36957,36959,36961],{},[1156,36958,1198],{},[1156,36960,1110],{},[1919,36962,2302],{},[1148,36964,1914],{},[1916,36966,36967,36983],{},[1145,36968,36969,36971,36973,36975,36977,36979,36981],{},[1919,36970,8789],{},[1148,36972,13255],{},[1919,36974,9232],{},[1148,36976,5066],{},[1919,36978,2644],{},[1148,36980,13255],{},[1919,36982,2614],{},[1919,36984,2187],{},[1148,36986,1914],{},[1919,36988,36989],{},"20,05",[1148,36991,1164],{"separator":1121},[1954,36993],{"width":1956},[1156,36995,12288],{},[1148,36997,1914],{},[1916,36999,37000,37008],{},[1145,37001,37002,37004,37006],{},[1919,37003,8822],{},[1148,37005,1990],{},[1919,37007,19846],{},[5460,37009,37010],{},[1919,37011,36989],{},[5460,37013,37014],{},[1916,37015,37016,37018],{},[1919,37017,2471],{},[1919,37019,7599],{},[1148,37021,14579],{},[1919,37023,37024],{},"3,651",[1148,37026,1164],{"separator":1121},[1954,37028],{"width":1956},[1156,37030,6835],{},[1148,37032,1914],{},[1148,37034,8536],{"stretchy":1150},[1148,37036,3636],{"stretchy":1150},[1156,37038,12288],{},[1148,37040,3636],{"stretchy":1150},[1148,37042,8553],{},[1217,37044,37045,37047],{},[1156,37046,12288],{},[1145,37048,37049,37051,37053],{},[1919,37050,2780],{},[1148,37052,1164],{"separator":1121},[1919,37054,36791],{},[1148,37056,1151],{"stretchy":1150},[1919,37058,2187],{},[1148,37060,1170],{"stretchy":1150},[1148,37062,8596],{"stretchy":1150},[1148,37064,1914],{},[1148,37066,8536],{"stretchy":1150},[1148,37068,3636],{"stretchy":1150},[1156,37070,12288],{},[1148,37072,3636],{"stretchy":1150},[1148,37074,8553],{},[1919,37076,37077],{},"2,086",[1148,37079,8596],{"stretchy":1150},[1172,37081,37082],{"encoding":1174},"s_p^2 = \\frac{9\\cdot 25 + 11\\cdot 16}{20} = 20{,}05, \\qquad t = \\frac{82-75}{\\sqrt{20{,}05}}\\sqrt{\\frac{120}{22}} \\approx 3{,}651, \\qquad W = \\{\\lvert t\\rvert \\ge t_{0,975}(20)\\} = \\{\\lvert t\\rvert \\ge 2{,}086\\}",[1110,37084,37085,11165,37102,37119],{},[1115,37086,37088],{"className":37087},[1136],[1138,37089,37090],{"xmlns":1140},[1142,37091,37092,37100],{},[1145,37093,37094,37096,37098],{},[1156,37095,12288],{},[1148,37097,12164],{},[1156,37099,6835],{},[1172,37101,33062],{"encoding":1174},[1115,37103,37105],{"className":37104},[1136],[1138,37106,37107],{"xmlns":1140},[1142,37108,37109,37117],{},[1145,37110,37111],{},[1217,37112,37113,37115],{},[1156,37114,6797],{},[1919,37116,2780],{},[1172,37118,6802],{"encoding":1174},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3261,37121,37123],{"className":3263,"code":37122,"language":71,"meta":3265,"style":3265},"s1 \u003C- 25; n1 \u003C- 10\ns2 \u003C- 16; n2 \u003C- 12\nFstat \u003C- s1 \u002F s2\nF_dolni \u003C- qf(0.025, n1 - 1, n2 - 1)\nF_horni \u003C- qf(0.975, n1 - 1, n2 - 1)\nFstat\nF_dolni\nF_horni\n",[1434,37124,37125,37143,37163,37178,37213,37244,37249,37254],{"__ignoreMap":3265},[1115,37126,37127,37130,37132,37134,37136,37139,37141],{"class":3270,"line":10},[1115,37128,37129],{"class":3280},"s1",[1115,37131,3291],{"class":3273},[1115,37133,19517],{"class":3312},[1115,37135,5832],{"class":3277},[1115,37137,37138],{"class":3280},"n1",[1115,37140,3291],{"class":3273},[1115,37142,34503],{"class":3312},[1115,37144,37145,37148,37150,37153,37155,37158,37160],{"class":3270,"line":27},[1115,37146,37147],{"class":3280},"s2",[1115,37149,3291],{"class":3273},[1115,37151,37152],{"class":3312}," 16",[1115,37154,5832],{"class":3277},[1115,37156,37157],{"class":3280},"n2",[1115,37159,3291],{"class":3273},[1115,37161,37162],{"class":3312}," 12\n",[1115,37164,37165,37168,37170,37173,37175],{"class":3270,"line":148},[1115,37166,37167],{"class":3280},"Fstat",[1115,37169,3291],{"class":3273},[1115,37171,37172],{"class":3280}," s1",[1115,37174,6292],{"class":3273},[1115,37176,37177],{"class":3280}," s2\n",[1115,37179,37180,37183,37185,37188,37190,37193,37195,37198,37200,37202,37204,37207,37209,37211],{"class":3270,"line":111},[1115,37181,37182],{"class":3280},"F_dolni",[1115,37184,3291],{"class":3273},[1115,37186,37187],{"class":3294}," qf",[1115,37189,1151],{"class":3277},[1115,37191,37192],{"class":3312},"0.025",[1115,37194,1164],{"class":3273},[1115,37196,37197],{"class":3280}," n1",[1115,37199,6178],{"class":3273},[1115,37201,3882],{"class":3312},[1115,37203,1164],{"class":3273},[1115,37205,37206],{"class":3280}," n2",[1115,37208,6178],{"class":3273},[1115,37210,3882],{"class":3312},[1115,37212,3283],{"class":3277},[1115,37214,37215,37218,37220,37222,37224,37226,37228,37230,37232,37234,37236,37238,37240,37242],{"class":3270,"line":96},[1115,37216,37217],{"class":3280},"F_horni",[1115,37219,3291],{"class":3273},[1115,37221,37187],{"class":3294},[1115,37223,1151],{"class":3277},[1115,37225,14231],{"class":3312},[1115,37227,1164],{"class":3273},[1115,37229,37197],{"class":3280},[1115,37231,6178],{"class":3273},[1115,37233,3882],{"class":3312},[1115,37235,1164],{"class":3273},[1115,37237,37206],{"class":3280},[1115,37239,6178],{"class":3273},[1115,37241,3882],{"class":3312},[1115,37243,3283],{"class":3277},[1115,37245,37246],{"class":3270,"line":89},[1115,37247,37248],{"class":3280},"Fstat\n",[1115,37250,37251],{"class":3270,"line":82},[1115,37252,37253],{"class":3280},"F_dolni\n",[1115,37255,37256],{"class":3270,"line":75},[1115,37257,37258],{"class":3280},"F_horni\n",[3261,37260,37263],{"className":37261,"code":37262,"language":4279,"meta":3265},[4277],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[1434,37264,37262],{"__ignoreMap":3265},[3261,37266,37268],{"className":3263,"code":37267,"language":71,"meta":3265,"style":3265},"sp2 \u003C- ((n1 - 1) * s1 + (n2 - 1) * s2) \u002F (n1 + n2 - 2)\nt \u003C- (82 - 75) \u002F sqrt(sp2) * sqrt(n1 * n2 \u002F (n1 + n2))\nt_krit \u003C- qt(0.975, df = n1 + n2 - 2)\nsp2\nt\nt_krit\n",[1434,37269,37270,37327,37378,37408,37413,37417],{"__ignoreMap":3265},[1115,37271,37272,37275,37277,37280,37282,37284,37286,37288,37290,37292,37294,37296,37298,37300,37302,37304,37306,37309,37311,37313,37315,37317,37319,37321,37323,37325],{"class":3270,"line":10},[1115,37273,37274],{"class":3280},"sp2",[1115,37276,3291],{"class":3273},[1115,37278,37279],{"class":3277}," ((",[1115,37281,37138],{"class":3280},[1115,37283,6178],{"class":3273},[1115,37285,3882],{"class":3312},[1115,37287,6207],{"class":3277},[1115,37289,9781],{"class":3273},[1115,37291,37172],{"class":3280},[1115,37293,6170],{"class":3273},[1115,37295,6173],{"class":3277},[1115,37297,37157],{"class":3280},[1115,37299,6178],{"class":3273},[1115,37301,3882],{"class":3312},[1115,37303,6207],{"class":3277},[1115,37305,9781],{"class":3273},[1115,37307,37308],{"class":3280}," s2",[1115,37310,6207],{"class":3277},[1115,37312,4412],{"class":3273},[1115,37314,6173],{"class":3277},[1115,37316,37138],{"class":3280},[1115,37318,6170],{"class":3273},[1115,37320,37206],{"class":3280},[1115,37322,6178],{"class":3273},[1115,37324,4156],{"class":3312},[1115,37326,3283],{"class":3277},[1115,37328,37329,37331,37333,37335,37337,37339,37342,37344,37346,37348,37350,37352,37354,37356,37358,37360,37362,37364,37366,37368,37370,37372,37374,37376],{"class":3270,"line":27},[1115,37330,12288],{"class":3280},[1115,37332,3291],{"class":3273},[1115,37334,6173],{"class":3277},[1115,37336,8822],{"class":3312},[1115,37338,6178],{"class":3273},[1115,37340,37341],{"class":3312}," 75",[1115,37343,6207],{"class":3277},[1115,37345,4412],{"class":3273},[1115,37347,6158],{"class":3294},[1115,37349,1151],{"class":3277},[1115,37351,37274],{"class":3280},[1115,37353,6207],{"class":3277},[1115,37355,9781],{"class":3273},[1115,37357,6158],{"class":3294},[1115,37359,1151],{"class":3277},[1115,37361,37138],{"class":3280},[1115,37363,6216],{"class":3273},[1115,37365,37206],{"class":3280},[1115,37367,6292],{"class":3273},[1115,37369,6173],{"class":3277},[1115,37371,37138],{"class":3280},[1115,37373,6170],{"class":3273},[1115,37375,37206],{"class":3280},[1115,37377,6019],{"class":3277},[1115,37379,37380,37382,37384,37386,37388,37390,37392,37394,37396,37398,37400,37402,37404,37406],{"class":3270,"line":148},[1115,37381,33169],{"class":3280},[1115,37383,3291],{"class":3273},[1115,37385,33174],{"class":3294},[1115,37387,1151],{"class":3277},[1115,37389,14231],{"class":3312},[1115,37391,1164],{"class":3273},[1115,37393,15941],{"class":3280},[1115,37395,3309],{"class":3273},[1115,37397,37197],{"class":3280},[1115,37399,6170],{"class":3273},[1115,37401,37206],{"class":3280},[1115,37403,6178],{"class":3273},[1115,37405,4156],{"class":3312},[1115,37407,3283],{"class":3277},[1115,37409,37410],{"class":3270,"line":111},[1115,37411,37412],{"class":3280},"sp2\n",[1115,37414,37415],{"class":3270,"line":96},[1115,37416,33199],{"class":3280},[1115,37418,37419],{"class":3270,"line":89},[1115,37420,33204],{"class":3280},[3261,37422,37425],{"className":37423,"code":37424,"language":4279,"meta":3265},[4277],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[1434,37426,37424],{"__ignoreMap":3265},[1110,37428,37429],{},[1527,37430],{"alt":37431,"className":37432,"src":37433},"mask-th-t-dvoustranny",[1531,1532],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,37435,37436,37437,1204,37440,37442,37443,37446,37447,1204,37464,4984,37481,37483,37484,37486],{},"V R provede obě kroky ",[1434,37438,37439],{},"var.test()",[1434,37441,32659],{},". Parametr ",[1434,37444,37445],{},"var.equal"," nastavuje volbu mezi ",[1115,37448,37450],{"className":37449},[1136],[1138,37451,37452],{"xmlns":1140},[1142,37453,37454,37462],{},[1145,37455,37456],{},[1217,37457,37458,37460],{},[1156,37459,5427],{},[1919,37461,1921],{},[1172,37463,36437],{"encoding":1174},[1115,37465,37467],{"className":37466},[1136],[1138,37468,37469],{"xmlns":1140},[1142,37470,37471,37479],{},[1145,37472,37473],{},[1217,37474,37475,37477],{},[1156,37476,5427],{},[1919,37478,2302],{},[1172,37480,36455],{"encoding":1174},[1434,37482,14662],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[1434,37485,14665],{}," předpoklad rozdílných rozptylů.",[1110,37488,37489,37492],{},[1445,37490,37491],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3261,37494,37496],{"className":3263,"code":37495,"language":71,"meta":3265,"style":3265},"A \u003C- c(313, 299, 315, 312, 310, 308, 314, 313, 305, 310, 309, 314)\nB \u003C- c(307, 322, 313, 313, 311, 316, 315, 314, 308, 319, 313, 312)\nvar.test(A, B)\nt.test(A, B, var.equal = TRUE)\n",[1434,37497,37498,37564,37627,37643],{"__ignoreMap":3265},[1115,37499,37500,37502,37504,37506,37508,37511,37513,37516,37518,37521,37523,37526,37528,37530,37532,37535,37537,37540,37542,37544,37546,37549,37551,37553,37555,37558,37560,37562],{"class":3270,"line":10},[1115,37501,7001],{"class":3280},[1115,37503,3291],{"class":3273},[1115,37505,4142],{"class":3294},[1115,37507,1151],{"class":3277},[1115,37509,37510],{"class":3312},"313",[1115,37512,1164],{"class":3273},[1115,37514,37515],{"class":3312}," 299",[1115,37517,1164],{"class":3273},[1115,37519,37520],{"class":3312}," 315",[1115,37522,1164],{"class":3273},[1115,37524,37525],{"class":3312}," 312",[1115,37527,1164],{"class":3273},[1115,37529,20481],{"class":3312},[1115,37531,1164],{"class":3273},[1115,37533,37534],{"class":3312}," 308",[1115,37536,1164],{"class":3273},[1115,37538,37539],{"class":3312}," 314",[1115,37541,1164],{"class":3273},[1115,37543,19278],{"class":3312},[1115,37545,1164],{"class":3273},[1115,37547,37548],{"class":3312}," 305",[1115,37550,1164],{"class":3273},[1115,37552,20481],{"class":3312},[1115,37554,1164],{"class":3273},[1115,37556,37557],{"class":3312}," 309",[1115,37559,1164],{"class":3273},[1115,37561,37539],{"class":3312},[1115,37563,3283],{"class":3277},[1115,37565,37566,37568,37570,37572,37574,37577,37579,37582,37584,37586,37588,37590,37592,37595,37597,37600,37602,37604,37606,37608,37610,37612,37614,37617,37619,37621,37623,37625],{"class":3270,"line":27},[1115,37567,7047],{"class":3280},[1115,37569,3291],{"class":3273},[1115,37571,4142],{"class":3294},[1115,37573,1151],{"class":3277},[1115,37575,37576],{"class":3312},"307",[1115,37578,1164],{"class":3273},[1115,37580,37581],{"class":3312}," 322",[1115,37583,1164],{"class":3273},[1115,37585,19278],{"class":3312},[1115,37587,1164],{"class":3273},[1115,37589,19278],{"class":3312},[1115,37591,1164],{"class":3273},[1115,37593,37594],{"class":3312}," 311",[1115,37596,1164],{"class":3273},[1115,37598,37599],{"class":3312}," 316",[1115,37601,1164],{"class":3273},[1115,37603,37520],{"class":3312},[1115,37605,1164],{"class":3273},[1115,37607,37539],{"class":3312},[1115,37609,1164],{"class":3273},[1115,37611,37534],{"class":3312},[1115,37613,1164],{"class":3273},[1115,37615,37616],{"class":3312}," 319",[1115,37618,1164],{"class":3273},[1115,37620,19278],{"class":3312},[1115,37622,1164],{"class":3273},[1115,37624,37525],{"class":3312},[1115,37626,3283],{"class":3277},[1115,37628,37629,37632,37634,37636,37638,37641],{"class":3270,"line":148},[1115,37630,37631],{"class":3294},"var.test",[1115,37633,1151],{"class":3277},[1115,37635,7001],{"class":3280},[1115,37637,1164],{"class":3273},[1115,37639,37640],{"class":3280}," B",[1115,37642,3283],{"class":3277},[1115,37644,37645,37647,37649,37651,37653,37655,37657,37660,37662,37664],{"class":3270,"line":111},[1115,37646,32724],{"class":3294},[1115,37648,1151],{"class":3277},[1115,37650,7001],{"class":3280},[1115,37652,1164],{"class":3273},[1115,37654,37640],{"class":3280},[1115,37656,1164],{"class":3273},[1115,37658,37659],{"class":3280}," var.equal",[1115,37661,3309],{"class":3273},[1115,37663,3313],{"class":3312},[1115,37665,3283],{"class":3277},[3261,37667,37670],{"className":37668,"code":37669,"language":4279,"meta":3265},[4277],"    F test to compare two variances\n\ndata:  A and B\nF = 1.1905, num df = 11, denom df = 11, p-value = 0.7776\nalternative hypothesis: true ratio of variances is not equal to 1\n95 percent confidence interval:\n 0.3427173 4.1354275\nsample estimates:\nratio of variances \n          1.190497 \n\n    Two Sample t-test\n\ndata:  A and B\nt = -1.9096, df = 22, p-value = 0.06932\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -7.1273286  0.2939953\nsample estimates:\nmean of x mean of y \n 310.1667  313.5833 \n",[1434,37671,37669],{"__ignoreMap":3265},[1110,37673,37674,37675,17176,37694,37697,37698,37717,37718,37735],{},"F-test shodu rozptylů nezamítá (",[1115,37676,37678],{"className":37677},[1136],[1138,37679,37680],{"xmlns":1140},[1142,37681,37682,37691],{},[1145,37683,37684,37686,37688],{},[1156,37685,1110],{},[1148,37687,1914],{},[1919,37689,37690],{},"0,7776",[1172,37692,37693],{"encoding":1174},"p = 0{,}7776",[1434,37695,37696],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,37699,37701],{"className":37700},[1136],[1138,37702,37703],{"xmlns":1140},[1142,37704,37705,37714],{},[1145,37706,37707,37709,37711],{},[1156,37708,1110],{},[1148,37710,1914],{},[1919,37712,37713],{},"0,06932",[1172,37715,37716],{"encoding":1174},"p = 0{,}06932"," — na hladině 5 % se ",[1115,37719,37721],{"className":37720},[1136],[1138,37722,37723],{"xmlns":1140},[1142,37724,37725,37733],{},[1145,37726,37727],{},[1217,37728,37729,37731],{},[1156,37730,6797],{},[1919,37732,2780],{},[1172,37734,6802],{"encoding":1174}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,37737,37738],{},[1445,37739,37740],{},"Výšky chlapců a dívek v páté třídě:",[3261,37742,37744],{"className":3263,"code":37743,"language":71,"meta":3265,"style":3265},"boys \u003C- c(130, 140, 136, 141, 139, 133, 149, 151, 139, 136, 138, 142, 127, 139, 147)\ngirls \u003C- c(135, 141, 143, 132, 146, 146, 151, 141, 141, 131, 142, 141)\nvar.test(boys, girls)\nt.test(boys, girls, var.equal = TRUE)\n",[1434,37745,37746,37826,37889,37904],{"__ignoreMap":3265},[1115,37747,37748,37751,37753,37755,37757,37760,37762,37764,37766,37769,37771,37774,37776,37779,37781,37784,37786,37788,37790,37792,37794,37796,37798,37800,37802,37805,37807,37810,37812,37815,37817,37819,37821,37824],{"class":3270,"line":10},[1115,37749,37750],{"class":3280},"boys",[1115,37752,3291],{"class":3273},[1115,37754,4142],{"class":3294},[1115,37756,1151],{"class":3277},[1115,37758,37759],{"class":3312},"130",[1115,37761,1164],{"class":3273},[1115,37763,20431],{"class":3312},[1115,37765,1164],{"class":3273},[1115,37767,37768],{"class":3312}," 136",[1115,37770,1164],{"class":3273},[1115,37772,37773],{"class":3312}," 141",[1115,37775,1164],{"class":3273},[1115,37777,37778],{"class":3312}," 139",[1115,37780,1164],{"class":3273},[1115,37782,37783],{"class":3312}," 133",[1115,37785,1164],{"class":3273},[1115,37787,23579],{"class":3312},[1115,37789,1164],{"class":3273},[1115,37791,19293],{"class":3312},[1115,37793,1164],{"class":3273},[1115,37795,37778],{"class":3312},[1115,37797,1164],{"class":3273},[1115,37799,37768],{"class":3312},[1115,37801,1164],{"class":3273},[1115,37803,37804],{"class":3312}," 138",[1115,37806,1164],{"class":3273},[1115,37808,37809],{"class":3312}," 142",[1115,37811,1164],{"class":3273},[1115,37813,37814],{"class":3312}," 127",[1115,37816,1164],{"class":3273},[1115,37818,37778],{"class":3312},[1115,37820,1164],{"class":3273},[1115,37822,37823],{"class":3312}," 147",[1115,37825,3283],{"class":3277},[1115,37827,37828,37831,37833,37835,37837,37839,37841,37843,37845,37848,37850,37853,37855,37858,37860,37862,37864,37866,37868,37870,37872,37874,37876,37879,37881,37883,37885,37887],{"class":3270,"line":27},[1115,37829,37830],{"class":3280},"girls",[1115,37832,3291],{"class":3273},[1115,37834,4142],{"class":3294},[1115,37836,1151],{"class":3277},[1115,37838,2419],{"class":3312},[1115,37840,1164],{"class":3273},[1115,37842,37773],{"class":3312},[1115,37844,1164],{"class":3273},[1115,37846,37847],{"class":3312}," 143",[1115,37849,1164],{"class":3273},[1115,37851,37852],{"class":3312}," 132",[1115,37854,1164],{"class":3273},[1115,37856,37857],{"class":3312}," 146",[1115,37859,1164],{"class":3273},[1115,37861,37857],{"class":3312},[1115,37863,1164],{"class":3273},[1115,37865,19293],{"class":3312},[1115,37867,1164],{"class":3273},[1115,37869,37773],{"class":3312},[1115,37871,1164],{"class":3273},[1115,37873,37773],{"class":3312},[1115,37875,1164],{"class":3273},[1115,37877,37878],{"class":3312}," 131",[1115,37880,1164],{"class":3273},[1115,37882,37809],{"class":3312},[1115,37884,1164],{"class":3273},[1115,37886,37773],{"class":3312},[1115,37888,3283],{"class":3277},[1115,37890,37891,37893,37895,37897,37899,37902],{"class":3270,"line":148},[1115,37892,37631],{"class":3294},[1115,37894,1151],{"class":3277},[1115,37896,37750],{"class":3280},[1115,37898,1164],{"class":3273},[1115,37900,37901],{"class":3280}," girls",[1115,37903,3283],{"class":3277},[1115,37905,37906,37908,37910,37912,37914,37916,37918,37920,37922,37924],{"class":3270,"line":111},[1115,37907,32724],{"class":3294},[1115,37909,1151],{"class":3277},[1115,37911,37750],{"class":3280},[1115,37913,1164],{"class":3273},[1115,37915,37901],{"class":3280},[1115,37917,1164],{"class":3273},[1115,37919,37659],{"class":3280},[1115,37921,3309],{"class":3273},[1115,37923,3313],{"class":3312},[1115,37925,3283],{"class":3277},[3261,37927,37930],{"className":37928,"code":37929,"language":4279,"meta":3265},[4277],"    F test to compare two variances\n\ndata:  boys and girls\nF = 1.2721, num df = 14, denom df = 11, p-value = 0.6977\nalternative hypothesis: true ratio of variances is not equal to 1\n95 percent confidence interval:\n 0.3787299 3.9365720\nsample estimates:\nratio of variances \n          1.272082 \n\n    Two Sample t-test\n\ndata:  boys and girls\nt = -0.70344, df = 25, p-value = 0.4883\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.67727  3.27727\nsample estimates:\nmean of x mean of y \n 139.1333  140.8333 \n",[1434,37931,37929],{"__ignoreMap":3265},[1110,37933,37674,37934,37953,37954,37956,37957,37976],{},[1115,37935,37937],{"className":37936},[1136],[1138,37938,37939],{"xmlns":1140},[1142,37940,37941,37950],{},[1145,37942,37943,37945,37947],{},[1156,37944,1110],{},[1148,37946,1914],{},[1919,37948,37949],{},"0,6977",[1172,37951,37952],{"encoding":1174},"p = 0{,}6977","), t-test s ",[1434,37955,37696],{}," dává ",[1115,37958,37960],{"className":37959},[1136],[1138,37961,37962],{"xmlns":1140},[1142,37963,37964,37973],{},[1145,37965,37966,37968,37970],{},[1156,37967,1110],{},[1148,37969,1914],{},[1919,37971,37972],{},"0,4883",[1172,37974,37975],{"encoding":1174},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1437,37978,37980],{"id":37979},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,37982,37983],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[1818,37985,37987],{"id":37986},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,37989,37990,37991,38014,38015,38034],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,37992,37994],{"className":37993},[1136],[1138,37995,37996],{"xmlns":1140},[1142,37997,37998,38012],{},[1145,37999,38000,38006,38008,38010],{},[1217,38001,38002,38004],{},[1156,38003,11867],{},[1156,38005,1292],{},[1148,38007,1151],{"stretchy":1150},[1156,38009,1158],{},[1148,38011,1170],{"stretchy":1150},[1172,38013,16313],{"encoding":1174}," s teoretickou distribuční funkcí ",[1115,38016,38018],{"className":38017},[1136],[1138,38019,38020],{"xmlns":1140},[1142,38021,38022,38032],{},[1145,38023,38024,38026,38028,38030],{},[1156,38025,11867],{},[1148,38027,1151],{"stretchy":1150},[1156,38029,1158],{},[1148,38031,1170],{"stretchy":1150},[1172,38033,12479],{"encoding":1174}," testovaného rozdělení.",[1124,38036,38037,38100,38120,38176],{},[1127,38038,38039,38056,38057,1204,38080,38099],{},[1115,38040,38042],{"className":38041},[1136],[1138,38043,38044],{"xmlns":1140},[1142,38045,38046,38054],{},[1145,38047,38048],{},[1217,38049,38050,38052],{},[1156,38051,6797],{},[1919,38053,2780],{},[1172,38055,6802],{"encoding":1174},": odchylky mezi ",[1115,38058,38060],{"className":38059},[1136],[1138,38061,38062],{"xmlns":1140},[1142,38063,38064,38078],{},[1145,38065,38066,38072,38074,38076],{},[1217,38067,38068,38070],{},[1156,38069,11867],{},[1156,38071,1292],{},[1148,38073,1151],{"stretchy":1150},[1156,38075,1158],{},[1148,38077,1170],{"stretchy":1150},[1172,38079,16313],{"encoding":1174},[1115,38081,38083],{"className":38082},[1136],[1138,38084,38085],{"xmlns":1140},[1142,38086,38087,38097],{},[1145,38088,38089,38091,38093,38095],{},[1156,38090,11867],{},[1148,38092,1151],{"stretchy":1150},[1156,38094,1158],{},[1148,38096,1170],{"stretchy":1150},[1172,38098,12479],{"encoding":1174}," jsou náhodné (data mají dané rozdělení).",[1127,38101,38102,38119],{},[1115,38103,38105],{"className":38104},[1136],[1138,38106,38107],{"xmlns":1140},[1142,38108,38109,38117],{},[1145,38110,38111],{},[1217,38112,38113,38115],{},[1156,38114,6797],{},[1919,38116,1921],{},[1172,38118,8200],{"encoding":1174},": data nemají dané rozdělení.",[1127,38121,38122,38123,1247],{},"Testové kritérium: ",[1115,38124,38126],{"className":38125},[1136],[1138,38127,38128],{"xmlns":1140},[1142,38129,38130,38173],{},[1145,38131,38132,38134,38136,38147,38149,38155,38157,38159,38161,38163,38165,38167,38169,38171],{},[1156,38133,13297],{},[1148,38135,1914],{},[1217,38137,38138,38145],{},[1145,38139,38140,38143],{},[1156,38141,38142],{},"sup",[1148,38144,1975],{},[1156,38146,1158],{},[1148,38148,3636],{"stretchy":1150},[1217,38150,38151,38153],{},[1156,38152,11867],{},[1156,38154,1292],{},[1148,38156,1151],{"stretchy":1150},[1156,38158,1158],{},[1148,38160,1170],{"stretchy":1150},[1148,38162,1990],{},[1156,38164,11867],{},[1148,38166,1151],{"stretchy":1150},[1156,38168,1158],{},[1148,38170,1170],{"stretchy":1150},[1148,38172,3636],{"stretchy":1150},[1172,38174,38175],{"encoding":1174},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1127,38177,8520,38178,38222,38223,38241,38242,1247],{},[1115,38179,38181],{"className":38180},[1136],[1138,38182,38183],{"xmlns":1140},[1142,38184,38185,38219],{},[1145,38186,38187,38193,38195,38197,38199,38201,38203,38205,38211,38213,38215,38217],{},[1217,38188,38189,38191],{},[1156,38190,6835],{},[1156,38192,8567],{},[1148,38194,1914],{},[1148,38196,8536],{"stretchy":1150},[1156,38198,12940],{},[1148,38200,2529],{},[1156,38202,12940],{},[1148,38204,5755],{},[1217,38206,38207,38209],{},[1156,38208,13297],{},[1156,38210,8567],{},[1148,38212,1151],{"stretchy":1150},[1156,38214,1292],{},[1148,38216,1170],{"stretchy":1150},[1148,38218,8596],{"stretchy":1150},[1172,38220,38221],{"encoding":1174},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,38224,38226],{"className":38225},[1136],[1138,38227,38228],{"xmlns":1140},[1142,38229,38230,38238],{},[1145,38231,38232,38234,38236],{},[1156,38233,1292],{},[1148,38235,5755],{},[1919,38237,2624],{},[1172,38239,38240],{"encoding":1174},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,38243,38245],{"className":38244},[1136],[1138,38246,38247],{"xmlns":1140},[1142,38248,38249,38260],{},[1145,38250,38251,38254,38256],{},[1919,38252,38253],{},"1,36",[1156,38255,4412],{"mathvariant":2014},[5460,38257,38258],{},[1156,38259,1292],{},[1172,38261,38262],{"encoding":1174},"1{,}36\u002F\\sqrt{n}",[1110,38264,32656,38265,38268,38269,38271,38272,1176,38275,38278],{},[1434,38266,38267],{},"ks.test()",", kde se za ",[1434,38270,12479],{}," dosadí příslušná distribuční funkce (",[1434,38273,38274],{},"\"pnorm\"",[1434,38276,38277],{},"\"pexp\"",", …) s jejími parametry:",[3261,38280,38282],{"className":3263,"code":38281,"language":71,"meta":3265,"style":3265},"x3 \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)\nks.test(x3, \"pnorm\", mean(x3), sd(x3))\n",[1434,38283,38284,38334],{"__ignoreMap":3265},[1115,38285,38286,38288,38290,38292,38294,38296,38298,38300,38302,38304,38306,38308,38310,38312,38314,38316,38318,38320,38322,38324,38326,38328,38330,38332],{"class":3270,"line":10},[1115,38287,33370],{"class":3280},[1115,38289,3291],{"class":3273},[1115,38291,4142],{"class":3294},[1115,38293,1151],{"class":3277},[1115,38295,17110],{"class":3312},[1115,38297,1164],{"class":3273},[1115,38299,17115],{"class":3312},[1115,38301,1164],{"class":3273},[1115,38303,17120],{"class":3312},[1115,38305,1164],{"class":3273},[1115,38307,17125],{"class":3312},[1115,38309,1164],{"class":3273},[1115,38311,17120],{"class":3312},[1115,38313,1164],{"class":3273},[1115,38315,17120],{"class":3312},[1115,38317,1164],{"class":3273},[1115,38319,17138],{"class":3312},[1115,38321,1164],{"class":3273},[1115,38323,17143],{"class":3312},[1115,38325,1164],{"class":3273},[1115,38327,17115],{"class":3312},[1115,38329,1164],{"class":3273},[1115,38331,17115],{"class":3312},[1115,38333,3283],{"class":3277},[1115,38335,38336,38339,38341,38343,38345,38348,38350,38352,38354,38356,38358,38360,38362,38364,38366],{"class":3270,"line":27},[1115,38337,38338],{"class":3294},"ks.test",[1115,38340,1151],{"class":3277},[1115,38342,33370],{"class":3280},[1115,38344,1164],{"class":3273},[1115,38346,38347],{"class":3300}," \"pnorm\"",[1115,38349,1164],{"class":3273},[1115,38351,6104],{"class":3294},[1115,38353,1151],{"class":3277},[1115,38355,33370],{"class":3280},[1115,38357,1170],{"class":3277},[1115,38359,1164],{"class":3273},[1115,38361,6012],{"class":3294},[1115,38363,1151],{"class":3277},[1115,38365,33370],{"class":3280},[1115,38367,6019],{"class":3277},[3261,38369,38372],{"className":38370,"code":38371,"language":4279,"meta":3265},[4277],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[1434,38373,38371],{"__ignoreMap":3265},[1110,38375,38376,38399],{},[1115,38377,38379],{"className":38378},[1136],[1138,38380,38381],{"xmlns":1140},[1142,38382,38383,38396],{},[1145,38384,38385,38387,38389,38392,38394],{},[1156,38386,1110],{},[1148,38388,1914],{},[1919,38390,38391],{},"0,8847",[1148,38393,5755],{},[1919,38395,9160],{},[1172,38397,38398],{"encoding":1174},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[1818,38401,38403],{"id":38402},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,38405,38406],{},"Nejpoužívanější a nejsilnější obecný test normality, citlivý na odchylky v šikmosti i špičatosti. Využívá korelaci mezi uspořádanými hodnotami výběru a jejich očekávanými hodnotami v normálním rozdělení.",[1124,38408,38409,38429,38449],{},[1127,38410,38411,38428],{},[1115,38412,38414],{"className":38413},[1136],[1138,38415,38416],{"xmlns":1140},[1142,38417,38418,38426],{},[1145,38419,38420],{},[1217,38421,38422,38424],{},[1156,38423,6797],{},[1919,38425,2780],{},[1172,38427,6802],{"encoding":1174},": data mají normální rozdělení.",[1127,38430,38431,38448],{},[1115,38432,38434],{"className":38433},[1136],[1138,38435,38436],{"xmlns":1140},[1142,38437,38438,38446],{},[1145,38439,38440],{},[1217,38441,38442,38444],{},[1156,38443,6797],{},[1919,38445,1921],{},[1172,38447,8200],{"encoding":1174},": data nemají normální rozdělení.",[1127,38450,38451,38452,38478],{},"Testová statistika ",[1115,38453,38455],{"className":38454},[1136],[1138,38456,38457],{"xmlns":1140},[1142,38458,38459,38475],{},[1145,38460,38461,38463,38465,38467,38469,38471,38473],{},[1156,38462,6835],{},[1148,38464,12164],{},[1148,38466,13568],{"stretchy":1150},[1919,38468,2780],{},[1148,38470,1164],{"separator":1121},[1919,38472,1921],{},[1148,38474,12587],{"stretchy":1150},[1172,38476,38477],{"encoding":1174},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,38480,38481,38482,38495,38496,6884,38516,38533,38534,6884,38554,38571],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,38483,38485],{"className":38484},[1136],[1138,38486,38487],{"xmlns":1140},[1142,38488,38489,38493],{},[1145,38490,38491],{},[1156,38492,6835],{},[1172,38494,6835],{"encoding":1174}," se běžně neudává): ",[1115,38497,38499],{"className":38498},[1136],[1138,38500,38501],{"xmlns":1140},[1142,38502,38503,38513],{},[1145,38504,38505,38507,38509,38511],{},[1156,38506,1110],{},[1148,38508,8553],{},[1156,38510,8567],{},[1148,38512,12693],{},[1172,38514,38515],{"encoding":1174},"p \\ge \\alpha \\Rightarrow",[1115,38517,38519],{"className":38518},[1136],[1138,38520,38521],{"xmlns":1140},[1142,38522,38523,38531],{},[1145,38524,38525],{},[1217,38526,38527,38529],{},[1156,38528,6797],{},[1919,38530,2780],{},[1172,38532,6802],{"encoding":1174}," nezamítáme (normalitu lze předpokládat); ",[1115,38535,38537],{"className":38536},[1136],[1138,38538,38539],{"xmlns":1140},[1142,38540,38541,38551],{},[1145,38542,38543,38545,38547,38549],{},[1156,38544,1110],{},[1148,38546,5682],{},[1156,38548,8567],{},[1148,38550,12693],{},[1172,38552,38553],{"encoding":1174},"p \u003C \\alpha \\Rightarrow",[1115,38555,38557],{"className":38556},[1136],[1138,38558,38559],{"xmlns":1140},[1142,38560,38561,38569],{},[1145,38562,38563],{},[1217,38564,38565,38567],{},[1156,38566,6797],{},[1919,38568,2780],{},[1172,38570,6802],{"encoding":1174}," zamítáme (předpoklad normality je porušen).",[3261,38573,38575],{"className":3263,"code":38574,"language":71,"meta":3265,"style":3265},"x2 \u003C- c(9.5, 10.5, 8.9, 9.2, 10.0, 8.5, 9.2, 8.8, 10.0, 9.5, 9.2)\nshapiro.test(x2)\n",[1434,38576,38577,38631],{"__ignoreMap":3265},[1115,38578,38579,38581,38583,38585,38587,38589,38591,38593,38595,38597,38599,38601,38603,38605,38607,38609,38611,38613,38615,38617,38619,38621,38623,38625,38627,38629],{"class":3270,"line":10},[1115,38580,33238],{"class":3280},[1115,38582,3291],{"class":3273},[1115,38584,4142],{"class":3294},[1115,38586,1151],{"class":3277},[1115,38588,33247],{"class":3312},[1115,38590,1164],{"class":3273},[1115,38592,33252],{"class":3312},[1115,38594,1164],{"class":3273},[1115,38596,33257],{"class":3312},[1115,38598,1164],{"class":3273},[1115,38600,33262],{"class":3312},[1115,38602,1164],{"class":3273},[1115,38604,33267],{"class":3312},[1115,38606,1164],{"class":3273},[1115,38608,33272],{"class":3312},[1115,38610,1164],{"class":3273},[1115,38612,33262],{"class":3312},[1115,38614,1164],{"class":3273},[1115,38616,33281],{"class":3312},[1115,38618,1164],{"class":3273},[1115,38620,33267],{"class":3312},[1115,38622,1164],{"class":3273},[1115,38624,33290],{"class":3312},[1115,38626,1164],{"class":3273},[1115,38628,33262],{"class":3312},[1115,38630,3283],{"class":3277},[1115,38632,38633,38635,38637,38639],{"class":3270,"line":27},[1115,38634,22684],{"class":3294},[1115,38636,1151],{"class":3277},[1115,38638,33238],{"class":3280},[1115,38640,3283],{"class":3277},[3261,38642,38645],{"className":38643,"code":38644,"language":4279,"meta":3265},[4277],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[1434,38646,38644],{"__ignoreMap":3265},[1110,38648,38649,38650,38669],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,38651,38653],{"className":38652},[1136],[1138,38654,38655],{"xmlns":1140},[1142,38656,38657,38666],{},[1145,38658,38659,38661,38663],{},[1156,38660,1110],{},[1148,38662,1914],{},[1919,38664,38665],{},"0,7744",[1172,38667,38668],{"encoding":1174},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,38671,38673,38680,38683,39050,39056],{"className":38672,"dataCallout":2145},[1106,2144],[1110,38674,38676,38679],{"className":38675},[1113],[1115,38677],{"className":38678,"ariaHidden":1121},[1118,2152,1120],"Příklad: Doba do poruchy výrobku",[1110,38681,38682],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3261,38684,38686],{"className":3263,"code":38685,"language":71,"meta":3265,"style":3265},"x9 \u003C- c(101, 338, 150, 47, 10, 2, 12, 392, 5, 73, 367, 54, 114, 213, 71, 341, 313, 112, 343, 151,\n        9, 160, 18, 113, 77, 71, 159, 12, 119, 130, 140, 161, 379, 54, 373, 168, 365, 110, 145,\n        88, 74, 46, 246, 259, 19, 119, 48, 3, 163, 179, 194, 33, 49, 501, 193, 19, 5, 2, 221, 300,\n        88, 13, 428, 249, 25, 209, 54, 91)\nmean(x9)\nsd(x9)\nmedian(x9)\nshapiro.test(x9)\nks.test(x9, \"pexp\", rate = 1 \u002F mean(x9))\n",[1434,38687,38688,38779,38857,38945,38979,38989,38999,39009,39019],{"__ignoreMap":3265},[1115,38689,38690,38692,38694,38696,38698,38700,38702,38704,38706,38708,38710,38712,38714,38716,38718,38720,38722,38724,38726,38728,38730,38732,38734,38736,38738,38741,38743,38745,38747,38749,38751,38753,38755,38757,38759,38761,38763,38765,38767,38769,38771,38773,38775,38777],{"class":3270,"line":10},[1115,38691,19193],{"class":3280},[1115,38693,3291],{"class":3273},[1115,38695,4142],{"class":3294},[1115,38697,1151],{"class":3277},[1115,38699,2369],{"class":3312},[1115,38701,1164],{"class":3273},[1115,38703,19206],{"class":3312},[1115,38705,1164],{"class":3273},[1115,38707,19211],{"class":3312},[1115,38709,1164],{"class":3273},[1115,38711,19216],{"class":3312},[1115,38713,1164],{"class":3273},[1115,38715,14616],{"class":3312},[1115,38717,1164],{"class":3273},[1115,38719,4156],{"class":3312},[1115,38721,1164],{"class":3273},[1115,38723,8919],{"class":3312},[1115,38725,1164],{"class":3273},[1115,38727,19233],{"class":3312},[1115,38729,1164],{"class":3273},[1115,38731,4161],{"class":3312},[1115,38733,1164],{"class":3273},[1115,38735,19242],{"class":3312},[1115,38737,1164],{"class":3273},[1115,38739,38740],{"class":3312}," 367",[1115,38742,1164],{"class":3273},[1115,38744,19254],{"class":3312},[1115,38746,1164],{"class":3273},[1115,38748,19259],{"class":3312},[1115,38750,1164],{"class":3273},[1115,38752,19264],{"class":3312},[1115,38754,1164],{"class":3273},[1115,38756,8937],{"class":3312},[1115,38758,1164],{"class":3273},[1115,38760,19273],{"class":3312},[1115,38762,1164],{"class":3273},[1115,38764,19278],{"class":3312},[1115,38766,1164],{"class":3273},[1115,38768,19283],{"class":3312},[1115,38770,1164],{"class":3273},[1115,38772,19288],{"class":3312},[1115,38774,1164],{"class":3273},[1115,38776,19293],{"class":3312},[1115,38778,8922],{"class":3273},[1115,38780,38781,38783,38785,38787,38789,38791,38793,38795,38797,38799,38801,38803,38805,38807,38809,38811,38813,38815,38817,38819,38821,38823,38825,38827,38829,38831,38833,38835,38837,38839,38841,38843,38845,38847,38849,38851,38853,38855],{"class":3270,"line":27},[1115,38782,19300],{"class":3312},[1115,38784,1164],{"class":3273},[1115,38786,19305],{"class":3312},[1115,38788,1164],{"class":3273},[1115,38790,19310],{"class":3312},[1115,38792,1164],{"class":3273},[1115,38794,19315],{"class":3312},[1115,38796,1164],{"class":3273},[1115,38798,19320],{"class":3312},[1115,38800,1164],{"class":3273},[1115,38802,8937],{"class":3312},[1115,38804,1164],{"class":3273},[1115,38806,19329],{"class":3312},[1115,38808,1164],{"class":3273},[1115,38810,8919],{"class":3312},[1115,38812,1164],{"class":3273},[1115,38814,19338],{"class":3312},[1115,38816,1164],{"class":3273},[1115,38818,19343],{"class":3312},[1115,38820,1164],{"class":3273},[1115,38822,20431],{"class":3312},[1115,38824,1164],{"class":3273},[1115,38826,19355],{"class":3312},[1115,38828,1164],{"class":3273},[1115,38830,19360],{"class":3312},[1115,38832,1164],{"class":3273},[1115,38834,19254],{"class":3312},[1115,38836,1164],{"class":3273},[1115,38838,19369],{"class":3312},[1115,38840,1164],{"class":3273},[1115,38842,19374],{"class":3312},[1115,38844,1164],{"class":3273},[1115,38846,19379],{"class":3312},[1115,38848,1164],{"class":3273},[1115,38850,5990],{"class":3312},[1115,38852,1164],{"class":3273},[1115,38854,19388],{"class":3312},[1115,38856,8922],{"class":3273},[1115,38858,38859,38861,38863,38866,38868,38870,38872,38874,38876,38878,38880,38882,38884,38886,38888,38890,38892,38894,38896,38898,38900,38902,38904,38907,38909,38911,38913,38915,38917,38919,38921,38923,38925,38927,38929,38931,38933,38935,38937,38939,38941,38943],{"class":3270,"line":148},[1115,38860,19498],{"class":3312},[1115,38862,1164],{"class":3273},[1115,38864,38865],{"class":3312}," 74",[1115,38867,1164],{"class":3273},[1115,38869,19405],{"class":3312},[1115,38871,1164],{"class":3273},[1115,38873,19410],{"class":3312},[1115,38875,1164],{"class":3273},[1115,38877,19415],{"class":3312},[1115,38879,1164],{"class":3273},[1115,38881,19420],{"class":3312},[1115,38883,1164],{"class":3273},[1115,38885,19338],{"class":3312},[1115,38887,1164],{"class":3273},[1115,38889,19429],{"class":3312},[1115,38891,1164],{"class":3273},[1115,38893,4197],{"class":3312},[1115,38895,1164],{"class":3273},[1115,38897,19438],{"class":3312},[1115,38899,1164],{"class":3273},[1115,38901,19443],{"class":3312},[1115,38903,1164],{"class":3273},[1115,38905,38906],{"class":3312}," 194",[1115,38908,1164],{"class":3273},[1115,38910,9319],{"class":3312},[1115,38912,1164],{"class":3273},[1115,38914,19459],{"class":3312},[1115,38916,1164],{"class":3273},[1115,38918,19464],{"class":3312},[1115,38920,1164],{"class":3273},[1115,38922,19469],{"class":3312},[1115,38924,1164],{"class":3273},[1115,38926,19420],{"class":3312},[1115,38928,1164],{"class":3273},[1115,38930,4161],{"class":3312},[1115,38932,1164],{"class":3273},[1115,38934,4156],{"class":3312},[1115,38936,1164],{"class":3273},[1115,38938,19486],{"class":3312},[1115,38940,1164],{"class":3273},[1115,38942,19491],{"class":3312},[1115,38944,8922],{"class":3273},[1115,38946,38947,38949,38951,38953,38955,38957,38959,38961,38963,38965,38967,38969,38971,38973,38975,38977],{"class":3270,"line":111},[1115,38948,19498],{"class":3312},[1115,38950,1164],{"class":3273},[1115,38952,8914],{"class":3312},[1115,38954,1164],{"class":3273},[1115,38956,19507],{"class":3312},[1115,38958,1164],{"class":3273},[1115,38960,19512],{"class":3312},[1115,38962,1164],{"class":3273},[1115,38964,19517],{"class":3312},[1115,38966,1164],{"class":3273},[1115,38968,19522],{"class":3312},[1115,38970,1164],{"class":3273},[1115,38972,19254],{"class":3312},[1115,38974,1164],{"class":3273},[1115,38976,19531],{"class":3312},[1115,38978,3283],{"class":3277},[1115,38980,38981,38983,38985,38987],{"class":3270,"line":96},[1115,38982,17260],{"class":3294},[1115,38984,1151],{"class":3277},[1115,38986,19193],{"class":3280},[1115,38988,3283],{"class":3277},[1115,38990,38991,38993,38995,38997],{"class":3270,"line":89},[1115,38992,17282],{"class":3294},[1115,38994,1151],{"class":3277},[1115,38996,19193],{"class":3280},[1115,38998,3283],{"class":3277},[1115,39000,39001,39003,39005,39007],{"class":3270,"line":82},[1115,39002,17978],{"class":3294},[1115,39004,1151],{"class":3277},[1115,39006,19193],{"class":3280},[1115,39008,3283],{"class":3277},[1115,39010,39011,39013,39015,39017],{"class":3270,"line":75},[1115,39012,22684],{"class":3294},[1115,39014,1151],{"class":3277},[1115,39016,19193],{"class":3280},[1115,39018,3283],{"class":3277},[1115,39020,39021,39023,39025,39027,39029,39032,39034,39036,39038,39040,39042,39044,39046,39048],{"class":3270,"line":9071},[1115,39022,38338],{"class":3294},[1115,39024,1151],{"class":3277},[1115,39026,19193],{"class":3280},[1115,39028,1164],{"class":3273},[1115,39030,39031],{"class":3300}," \"pexp\"",[1115,39033,1164],{"class":3273},[1115,39035,15202],{"class":3280},[1115,39037,3309],{"class":3273},[1115,39039,3882],{"class":3312},[1115,39041,6292],{"class":3273},[1115,39043,6104],{"class":3294},[1115,39045,1151],{"class":3277},[1115,39047,19193],{"class":3280},[1115,39049,6019],{"class":3277},[3261,39051,39054],{"className":39052,"code":39053,"language":4279,"meta":3265},[4277],"[1] 145.4412\n[1] 126.1283\n[1] 113.5\n\n    Shapiro-Wilk normality test\n\ndata:  x9\nW = 0.89872, p-value = 4.389e-05\n\n    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x9\nD = 0.074727, p-value = 0.8421\nalternative hypothesis: two-sided\n",[1434,39055,39053],{"__ignoreMap":3265},[1110,39057,39058,39059,39078,39079,39096,39097,39116],{},"Výběrový průměr (145,44 min) je blízký směrodatné odchylce (126,13 min) a medián (113,5 min) je výrazně nižší než průměr — typický tvar doby do poruchy. Shapiro-Wilkův test normalitu jasně zamítá (",[1115,39060,39062],{"className":39061},[1136],[1138,39063,39064],{"xmlns":1140},[1142,39065,39066,39075],{},[1145,39067,39068,39070,39072],{},[1156,39069,1110],{},[1148,39071,5682],{},[1919,39073,39074],{},"0,0001",[1172,39076,39077],{"encoding":1174},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,39080,39082],{"className":39081},[1136],[1138,39083,39084],{"xmlns":1140},[1142,39085,39086,39094],{},[1145,39087,39088],{},[1153,39089,39090,39092],{"accent":1121},[1156,39091,1158],{},[1148,39093,1161],{},[1172,39095,2136],{"encoding":1174}," shodu nezamítá (",[1115,39098,39100],{"className":39099},[1136],[1138,39101,39102],{"xmlns":1140},[1142,39103,39104,39113],{},[1145,39105,39106,39108,39110],{},[1156,39107,1110],{},[1148,39109,1914],{},[1919,39111,39112],{},"0,8421",[1172,39114,39115],{"encoding":1174},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,39118,39119],{},[1527,39120],{"alt":39121,"className":39122,"src":39123},"mask-th-exponencialni-shoda",[1531,1532],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1437,39125,39127],{"id":39126},"neparametrické-testy","Neparametrické testy",[1110,39129,39130,39131,6173,39133,39157],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1445,39132,16678],{},[1115,39134,39136],{"className":39135},[1136],[1138,39137,39138],{"xmlns":1140},[1142,39139,39140,39154],{},[1145,39141,39142],{},[1217,39143,39144,39146],{},[1156,39145,1158],{},[1145,39147,39148,39150,39152],{},[1919,39149,2780],{},[1148,39151,1164],{"separator":1121},[1919,39153,2424],{},[1172,39155,39156],{"encoding":1174},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[1818,39159,39161],{"id":39160},"wilcoxonovy-testy","Wilcoxonovy testy",[1459,39163,39164,39209],{},[1462,39165,39166],{},[1465,39167,39168,39187,39206],{},[1468,39169,39170],{},[1115,39171,39173],{"className":39172},[1136],[1138,39174,39175],{"xmlns":1140},[1142,39176,39177,39185],{},[1145,39178,39179],{},[1217,39180,39181,39183],{},[1156,39182,6797],{},[1919,39184,2780],{},[1172,39186,6802],{"encoding":1174},[1468,39188,39189],{},[1115,39190,39192],{"className":39191},[1136],[1138,39193,39194],{"xmlns":1140},[1142,39195,39196,39204],{},[1145,39197,39198],{},[1217,39199,39200,39202],{},[1156,39201,6797],{},[1919,39203,1921],{},[1172,39205,8200],{"encoding":1174},[1468,39207,39208],{},"Příkaz v R",[1477,39210,39211,39278,39345],{},[1465,39212,39213,39243,39273],{},[1482,39214,39215],{},[1115,39216,39218],{"className":39217},[1136],[1138,39219,39220],{"xmlns":1140},[1142,39221,39222,39240],{},[1145,39223,39224,39236,39238],{},[1217,39225,39226,39228],{},[1156,39227,1158],{},[1145,39229,39230,39232,39234],{},[1919,39231,2780],{},[1148,39233,1164],{"separator":1121},[1919,39235,2424],{},[1148,39237,11884],{},[1156,39239,1262],{},[1172,39241,39242],{"encoding":1174},"x_{0,5} \\le c",[1482,39244,39245],{},[1115,39246,39248],{"className":39247},[1136],[1138,39249,39250],{"xmlns":1140},[1142,39251,39252,39270],{},[1145,39253,39254,39266,39268],{},[1217,39255,39256,39258],{},[1156,39257,1158],{},[1145,39259,39260,39262,39264],{},[1919,39261,2780],{},[1148,39263,1164],{"separator":1121},[1919,39265,2424],{},[1148,39267,5755],{},[1156,39269,1262],{},[1172,39271,39272],{"encoding":1174},"x_{0,5} > c",[1482,39274,39275],{},[1434,39276,39277],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1465,39279,39280,39310,39340],{},[1482,39281,39282],{},[1115,39283,39285],{"className":39284},[1136],[1138,39286,39287],{"xmlns":1140},[1142,39288,39289,39307],{},[1145,39290,39291,39303,39305],{},[1217,39292,39293,39295],{},[1156,39294,1158],{},[1145,39296,39297,39299,39301],{},[1919,39298,2780],{},[1148,39300,1164],{"separator":1121},[1919,39302,2424],{},[1148,39304,1914],{},[1156,39306,1262],{},[1172,39308,39309],{"encoding":1174},"x_{0,5} = c",[1482,39311,39312],{},[1115,39313,39315],{"className":39314},[1136],[1138,39316,39317],{"xmlns":1140},[1142,39318,39319,39337],{},[1145,39320,39321,39333,39335],{},[1217,39322,39323,39325],{},[1156,39324,1158],{},[1145,39326,39327,39329,39331],{},[1919,39328,2780],{},[1148,39330,1164],{"separator":1121},[1919,39332,2424],{},[1148,39334,16087],{"mathvariant":2014},[1156,39336,1262],{},[1172,39338,39339],{"encoding":1174},"x_{0,5} \\neq c",[1482,39341,39342],{},[1434,39343,39344],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1465,39346,39347,39377,39407],{},[1482,39348,39349],{},[1115,39350,39352],{"className":39351},[1136],[1138,39353,39354],{"xmlns":1140},[1142,39355,39356,39374],{},[1145,39357,39358,39370,39372],{},[1217,39359,39360,39362],{},[1156,39361,1158],{},[1145,39363,39364,39366,39368],{},[1919,39365,2780],{},[1148,39367,1164],{"separator":1121},[1919,39369,2424],{},[1148,39371,8553],{},[1156,39373,1262],{},[1172,39375,39376],{"encoding":1174},"x_{0,5} \\ge c",[1482,39378,39379],{},[1115,39380,39382],{"className":39381},[1136],[1138,39383,39384],{"xmlns":1140},[1142,39385,39386,39404],{},[1145,39387,39388,39400,39402],{},[1217,39389,39390,39392],{},[1156,39391,1158],{},[1145,39393,39394,39396,39398],{},[1919,39395,2780],{},[1148,39397,1164],{"separator":1121},[1919,39399,2424],{},[1148,39401,5682],{},[1156,39403,1262],{},[1172,39405,39406],{"encoding":1174},"x_{0,5} \u003C c",[1482,39408,39409],{},[1434,39410,39411],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,39413,39414,39417,39418,1247],{},[6671,39415,39416],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,39419,39421],{"className":39420},[1136],[1138,39422,39423],{"xmlns":1140},[1142,39424,39425,39429],{},[1145,39426,39427],{},[1156,39428,1262],{},[1172,39430,1262],{"encoding":1174},[1110,39432,39433,39436,39437,13976,39475,39488,39489,1247],{},[6671,39434,39435],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,39438,39440],{"className":39439},[1136],[1138,39441,39442],{"xmlns":1140},[1142,39443,39444,39472],{},[1145,39445,39446,39458,39460],{},[1217,39447,39448,39450],{},[1156,39449,1158],{},[1145,39451,39452,39454,39456],{},[1919,39453,2780],{},[1148,39455,1164],{"separator":1121},[1919,39457,2424],{},[1148,39459,1990],{},[1217,39461,39462,39464],{},[1156,39463,12274],{},[1145,39465,39466,39468,39470],{},[1919,39467,2780],{},[1148,39469,1164],{"separator":1121},[1919,39471,2424],{},[1172,39473,39474],{"encoding":1174},"x_{0,5}-y_{0,5}",[1115,39476,39478],{"className":39477},[1136],[1138,39479,39480],{"xmlns":1140},[1142,39481,39482,39486],{},[1145,39483,39484],{},[1156,39485,1262],{},[1172,39487,1262],{"encoding":1174},"; v R se volá se stejnými argumenty jako výše a navíc ",[1434,39490,39491],{},"paired = TRUE",[1110,39493,39494,39497,39498,39500],{},[6671,39495,39496],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[1434,39499,6099],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3261,39502,39504],{"className":3263,"code":39503,"language":71,"meta":3265,"style":3265},"boys \u003C- c(130, 140, 136, 141, 139, 133, 149, 151, 139, 136, 138, 142, 127, 139, 147)\ngirls \u003C- c(135, 141, 143, 132, 146, 146, 151, 141, 141, 131, 142, 141)\nwilcox.test(boys, girls, alternative = \"two.sided\")\n",[1434,39505,39506,39576,39634],{"__ignoreMap":3265},[1115,39507,39508,39510,39512,39514,39516,39518,39520,39522,39524,39526,39528,39530,39532,39534,39536,39538,39540,39542,39544,39546,39548,39550,39552,39554,39556,39558,39560,39562,39564,39566,39568,39570,39572,39574],{"class":3270,"line":10},[1115,39509,37750],{"class":3280},[1115,39511,3291],{"class":3273},[1115,39513,4142],{"class":3294},[1115,39515,1151],{"class":3277},[1115,39517,37759],{"class":3312},[1115,39519,1164],{"class":3273},[1115,39521,20431],{"class":3312},[1115,39523,1164],{"class":3273},[1115,39525,37768],{"class":3312},[1115,39527,1164],{"class":3273},[1115,39529,37773],{"class":3312},[1115,39531,1164],{"class":3273},[1115,39533,37778],{"class":3312},[1115,39535,1164],{"class":3273},[1115,39537,37783],{"class":3312},[1115,39539,1164],{"class":3273},[1115,39541,23579],{"class":3312},[1115,39543,1164],{"class":3273},[1115,39545,19293],{"class":3312},[1115,39547,1164],{"class":3273},[1115,39549,37778],{"class":3312},[1115,39551,1164],{"class":3273},[1115,39553,37768],{"class":3312},[1115,39555,1164],{"class":3273},[1115,39557,37804],{"class":3312},[1115,39559,1164],{"class":3273},[1115,39561,37809],{"class":3312},[1115,39563,1164],{"class":3273},[1115,39565,37814],{"class":3312},[1115,39567,1164],{"class":3273},[1115,39569,37778],{"class":3312},[1115,39571,1164],{"class":3273},[1115,39573,37823],{"class":3312},[1115,39575,3283],{"class":3277},[1115,39577,39578,39580,39582,39584,39586,39588,39590,39592,39594,39596,39598,39600,39602,39604,39606,39608,39610,39612,39614,39616,39618,39620,39622,39624,39626,39628,39630,39632],{"class":3270,"line":27},[1115,39579,37830],{"class":3280},[1115,39581,3291],{"class":3273},[1115,39583,4142],{"class":3294},[1115,39585,1151],{"class":3277},[1115,39587,2419],{"class":3312},[1115,39589,1164],{"class":3273},[1115,39591,37773],{"class":3312},[1115,39593,1164],{"class":3273},[1115,39595,37847],{"class":3312},[1115,39597,1164],{"class":3273},[1115,39599,37852],{"class":3312},[1115,39601,1164],{"class":3273},[1115,39603,37857],{"class":3312},[1115,39605,1164],{"class":3273},[1115,39607,37857],{"class":3312},[1115,39609,1164],{"class":3273},[1115,39611,19293],{"class":3312},[1115,39613,1164],{"class":3273},[1115,39615,37773],{"class":3312},[1115,39617,1164],{"class":3273},[1115,39619,37773],{"class":3312},[1115,39621,1164],{"class":3273},[1115,39623,37878],{"class":3312},[1115,39625,1164],{"class":3273},[1115,39627,37809],{"class":3312},[1115,39629,1164],{"class":3273},[1115,39631,37773],{"class":3312},[1115,39633,3283],{"class":3277},[1115,39635,39636,39639,39641,39643,39645,39647,39649,39651,39653,39655],{"class":3270,"line":148},[1115,39637,39638],{"class":3294},"wilcox.test",[1115,39640,1151],{"class":3277},[1115,39642,37750],{"class":3280},[1115,39644,1164],{"class":3273},[1115,39646,37901],{"class":3280},[1115,39648,1164],{"class":3273},[1115,39650,32741],{"class":3280},[1115,39652,3309],{"class":3273},[1115,39654,32746],{"class":3300},[1115,39656,3283],{"class":3277},[3261,39658,39661],{"className":39659,"code":39660,"language":4279,"meta":3265},[4277],"    Wilcoxon rank sum exact test\n\ndata:  boys and girls\nW = 69, p-value = 0.315\nalternative hypothesis: true location shift is not equal to 0\n",[1434,39662,39660],{"__ignoreMap":3265},[1110,39664,39665,39688],{},[1115,39666,39668],{"className":39667},[1136],[1138,39669,39670],{"xmlns":1140},[1142,39671,39672,39685],{},[1145,39673,39674,39676,39678,39681,39683],{},[1156,39675,1110],{},[1148,39677,1914],{},[1919,39679,39680],{},"0,315",[1148,39682,5755],{},[1919,39684,9160],{},[1172,39686,39687],{"encoding":1174},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,39690,39692,39699,39721,39832,39838],{"className":39691,"dataCallout":2145},[1106,2144],[1110,39693,39695,39698],{"className":39694},[1113],[1115,39696],{"className":39697,"ariaHidden":1121},[1118,2152,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,39700,39701,39702,39720],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,39703,39705],{"className":39704},[1136],[1138,39706,39707],{"xmlns":1140},[1142,39708,39709,39717],{},[1145,39710,39711,39713,39715],{},[1156,39712,1110],{},[1148,39714,1914],{},[1919,39716,34794],{},[1172,39718,39719],{"encoding":1174},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3261,39722,39724],{"className":3263,"code":39723,"language":71,"meta":3265,"style":3265},"estA \u003C- c(3282, 2506, 2812, 5453, 3263, 4571, 3121, 2963)\nestB \u003C- c(3271, 2531, 2799, 5471, 3285, 4557, 3139, 2976)\nwilcox.test(estA, estB, paired = TRUE)\n",[1434,39725,39726,39768,39810],{"__ignoreMap":3265},[1115,39727,39728,39730,39732,39734,39736,39738,39740,39742,39744,39746,39748,39750,39752,39754,39756,39758,39760,39762,39764,39766],{"class":3270,"line":10},[1115,39729,34597],{"class":3280},[1115,39731,3291],{"class":3273},[1115,39733,4142],{"class":3294},[1115,39735,1151],{"class":3277},[1115,39737,34606],{"class":3312},[1115,39739,1164],{"class":3273},[1115,39741,34611],{"class":3312},[1115,39743,1164],{"class":3273},[1115,39745,34616],{"class":3312},[1115,39747,1164],{"class":3273},[1115,39749,34621],{"class":3312},[1115,39751,1164],{"class":3273},[1115,39753,34626],{"class":3312},[1115,39755,1164],{"class":3273},[1115,39757,34631],{"class":3312},[1115,39759,1164],{"class":3273},[1115,39761,34636],{"class":3312},[1115,39763,1164],{"class":3273},[1115,39765,34641],{"class":3312},[1115,39767,3283],{"class":3277},[1115,39769,39770,39772,39774,39776,39778,39780,39782,39784,39786,39788,39790,39792,39794,39796,39798,39800,39802,39804,39806,39808],{"class":3270,"line":27},[1115,39771,34648],{"class":3280},[1115,39773,3291],{"class":3273},[1115,39775,4142],{"class":3294},[1115,39777,1151],{"class":3277},[1115,39779,34657],{"class":3312},[1115,39781,1164],{"class":3273},[1115,39783,34662],{"class":3312},[1115,39785,1164],{"class":3273},[1115,39787,34667],{"class":3312},[1115,39789,1164],{"class":3273},[1115,39791,34672],{"class":3312},[1115,39793,1164],{"class":3273},[1115,39795,34677],{"class":3312},[1115,39797,1164],{"class":3273},[1115,39799,34682],{"class":3312},[1115,39801,1164],{"class":3273},[1115,39803,34687],{"class":3312},[1115,39805,1164],{"class":3273},[1115,39807,34692],{"class":3312},[1115,39809,3283],{"class":3277},[1115,39811,39812,39814,39816,39818,39820,39822,39824,39826,39828,39830],{"class":3270,"line":148},[1115,39813,39638],{"class":3294},[1115,39815,1151],{"class":3277},[1115,39817,34597],{"class":3280},[1115,39819,1164],{"class":3273},[1115,39821,34707],{"class":3280},[1115,39823,1164],{"class":3273},[1115,39825,34712],{"class":3280},[1115,39827,3309],{"class":3273},[1115,39829,3313],{"class":3312},[1115,39831,3283],{"class":3277},[3261,39833,39836],{"className":39834,"code":39835,"language":4279,"meta":3265},[4277],"    Wilcoxon signed rank exact test\n\ndata:  estA and estB\nV = 7.5, p-value = 0.1484\nalternative hypothesis: true location shift is not equal to 0\n",[1434,39837,39835],{"__ignoreMap":3265},[1110,39839,39840,39863],{},[1115,39841,39843],{"className":39842},[1136],[1138,39844,39845],{"xmlns":1140},[1142,39846,39847,39860],{},[1145,39848,39849,39851,39853,39856,39858],{},[1156,39850,1110],{},[1148,39852,1914],{},[1919,39854,39855],{},"0,1484",[1148,39857,5755],{},[1919,39859,9160],{},[1172,39861,39862],{"encoding":1174},"p = 0{,}1484 > 0{,}05",": medián diferencí se od nuly statisticky významně neliší, odhadci se neliší. Závěr je stejný jako u (nespolehlivého) párového t-testu, ale tady je podložený testem, jehož předpoklady data splňují.",[1818,39865,39867],{"id":39866},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,39869,39870,39871,39888],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,39872,39874],{"className":39873},[1136],[1138,39875,39876],{"xmlns":1140},[1142,39877,39878,39886],{},[1145,39879,39880],{},[1217,39881,39882,39884],{},[1156,39883,6797],{},[1919,39885,2780],{},[1172,39887,6802],{"encoding":1174},": všechny výběry pocházejí ze stejného rozdělení.",[3261,39890,39892],{"className":3263,"code":39891,"language":71,"meta":3265,"style":3265},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[1434,39893,39894],{"__ignoreMap":3265},[1115,39895,39896,39899,39901,39904,39906,39909,39911,39913,39915,39918],{"class":3270,"line":10},[1115,39897,39898],{"class":3294},"kruskal.test",[1115,39900,1151],{"class":3277},[1115,39902,39903],{"class":3280},"kvantitativní_proměnná",[1115,39905,21968],{"class":3273},[1115,39907,39908],{"class":3280}," faktor",[1115,39910,1164],{"class":3273},[1115,39912,4514],{"class":3280},[1115,39914,3309],{"class":3273},[1115,39916,39917],{"class":3280}," soubor",[1115,39919,3283],{"class":3277},[1818,39921,39923],{"id":39922},"mediánový-test","Mediánový test",[1110,39925,39926,39927,39944,39945,2529],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,39928,39930],{"className":39929},[1136],[1138,39931,39932],{"xmlns":1140},[1142,39933,39934,39942],{},[1145,39935,39936],{},[1217,39937,39938,39940],{},[1156,39939,6797],{},[1919,39941,2780],{},[1172,39943,6802],{"encoding":1174},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[1434,39946,39947],{},"agricolae",[3261,39949,39951],{"className":3263,"code":39950,"language":71,"meta":3265,"style":3265},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[1434,39952,39953,39963],{"__ignoreMap":3265},[1115,39954,39955,39957,39959,39961],{"class":3270,"line":10},[1115,39956,3274],{"class":3273},[1115,39958,1151],{"class":3277},[1115,39960,39947],{"class":3280},[1115,39962,3283],{"class":3277},[1115,39964,39965,39968,39970,39972,39974,39976],{"class":3270,"line":27},[1115,39966,39967],{"class":3294},"Median.test",[1115,39969,1151],{"class":3277},[1115,39971,39903],{"class":3280},[1115,39973,1164],{"class":3273},[1115,39975,39908],{"class":3280},[1115,39977,3283],{"class":3277},[1818,39979,39981],{"id":39980},"friedmanův-test","Friedmanův test",[1110,39983,39984,39985,40002,40003,40041],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,39986,39988],{"className":39987},[1136],[1138,39989,39990],{"xmlns":1140},[1142,39991,39992,40000],{},[1145,39993,39994],{},[1217,39995,39996,39998],{},[1156,39997,6797],{},[1919,39999,2780],{},[1172,40001,6802],{"encoding":1174},": distribuční funkce veličin ",[1115,40004,40006],{"className":40005},[1136],[1138,40007,40008],{"xmlns":1140},[1142,40009,40010,40038],{},[1145,40011,40012,40022,40024,40026,40028],{},[1217,40013,40014,40016],{},[1156,40015,2168],{},[1145,40017,40018,40020],{},[1156,40019,1223],{},[1919,40021,1921],{},[1148,40023,1164],{"separator":1121},[1148,40025,2043],{},[1148,40027,1164],{"separator":1121},[1217,40029,40030,40032],{},[1156,40031,2168],{},[1145,40033,40034,40036],{},[1156,40035,1223],{},[1156,40037,1234],{},[1172,40039,40040],{"encoding":1174},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3261,40043,40045],{"className":3263,"code":40044,"language":71,"meta":3265,"style":3265},"friedman.test(kvantitativní_proměnná ~ faktor_A | faktor_B, data = soubor)\n# jsou-li proměnné samostatné vektory (bez argumentu data):\nfriedman.test(kvantitativní_proměnná, faktor_A, faktor_B)\n",[1434,40046,40047,40077,40082],{"__ignoreMap":3265},[1115,40048,40049,40052,40054,40056,40058,40061,40064,40067,40069,40071,40073,40075],{"class":3270,"line":10},[1115,40050,40051],{"class":3294},"friedman.test",[1115,40053,1151],{"class":3277},[1115,40055,39903],{"class":3280},[1115,40057,21968],{"class":3273},[1115,40059,40060],{"class":3280}," faktor_A",[1115,40062,40063],{"class":3273}," |",[1115,40065,40066],{"class":3280}," faktor_B",[1115,40068,1164],{"class":3273},[1115,40070,4514],{"class":3280},[1115,40072,3309],{"class":3273},[1115,40074,39917],{"class":3280},[1115,40076,3283],{"class":3277},[1115,40078,40079],{"class":3270,"line":27},[1115,40080,40081],{"class":3339},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,40083,40084,40086,40088,40090,40092,40094,40096,40098],{"class":3270,"line":148},[1115,40085,40051],{"class":3294},[1115,40087,1151],{"class":3277},[1115,40089,39903],{"class":3280},[1115,40091,1164],{"class":3273},[1115,40093,40060],{"class":3280},[1115,40095,1164],{"class":3273},[1115,40097,40066],{"class":3280},[1115,40099,3283],{"class":3277},[1437,40101,40103],{"id":40102},"přehled-testů","Přehled testů",[1110,40105,40106],{},[1527,40107],{"alt":40108,"className":40109,"src":40110},"mask-ilu-volba-testu",[1531,1532],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1459,40112,40113,40126],{},[1462,40114,40115],{},[1465,40116,40117,40120,40123],{},[1468,40118,40119],{},"Situace",[1468,40121,40122],{},"Test",[1468,40124,40125],{},"R funkce",[1477,40127,40128,40141,40154,40166,40179,40194,40206,40219,40232,40245,40257,40272],{},[1465,40129,40130,40133,40136],{},[1482,40131,40132],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1482,40134,40135],{},"jednovýběrový t-test",[1482,40137,40138],{},[1434,40139,40140],{},"t.test(x, mu = ..., alternative = ...)",[1465,40142,40143,40146,40149],{},[1482,40144,40145],{},"Rozdíl dvou závislých měření, diference normální",[1482,40147,40148],{},"párový t-test",[1482,40150,40151],{},[1434,40152,40153],{},"t.test(x, y, paired = TRUE)",[1465,40155,40156,40159,40161],{},[1482,40157,40158],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1482,40160,25179],{},[1482,40162,40163],{},[1434,40164,40165],{},"var.test(x, y)",[1465,40167,40168,40171,40174],{},[1482,40169,40170],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1482,40172,40173],{},"dvouvýběrový t-test",[1482,40175,40176],{},[1434,40177,40178],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1465,40180,40181,40184,40186],{},[1482,40182,40183],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1482,40185,37987],{},[1482,40187,40188,1176,40191],{},[1434,40189,40190],{},"ks.test(x, \"pnorm\", mu, sigma)",[1434,40192,40193],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1465,40195,40196,40199,40201],{},[1482,40197,40198],{},"Normalita dat",[1482,40200,38403],{},[1482,40202,40203],{},[1434,40204,40205],{},"shapiro.test(x)",[1465,40207,40208,40211,40214],{},[1482,40209,40210],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1482,40212,40213],{},"jednovýběrový Wilcoxonův test",[1482,40215,40216],{},[1434,40217,40218],{},"wilcox.test(x, mu = c, alternative = ...)",[1465,40220,40221,40224,40227],{},[1482,40222,40223],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1482,40225,40226],{},"párový Wilcoxonův test",[1482,40228,40229],{},[1434,40230,40231],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1465,40233,40234,40237,40240],{},[1482,40235,40236],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1482,40238,40239],{},"dvouvýběrový Wilcoxonův test",[1482,40241,40242],{},[1434,40243,40244],{},"wilcox.test(x, y)",[1465,40246,40247,40250,40252],{},[1482,40248,40249],{},"Více než dva nezávislé výběry, data nejsou normální",[1482,40251,39867],{},[1482,40253,40254],{},[1434,40255,40256],{},"kruskal.test(y ~ faktor, data)",[1465,40258,40259,40262,40265],{},[1482,40260,40261],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1482,40263,40264],{},"mediánový test",[1482,40266,40267,3256,40270],{},[1434,40268,40269],{},"Median.test(y, faktor)",[1434,40271,39947],{},[1465,40273,40274,40277,40279],{},[1482,40275,40276],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1482,40278,39981],{},[1482,40280,40281],{},[1434,40282,40283],{},"friedman.test(y ~ A | B, data)",[1437,40285,6378],{"id":6377},[1124,40287,40288,40365,40371,40388,40419],{},[1127,40289,40290,40329,40330,37717,40347,40364],{},[1445,40291,40292,40293,40310,40311,40328],{},"Nezamítnutí ",[1115,40294,40296],{"className":40295},[1136],[1138,40297,40298],{"xmlns":1140},[1142,40299,40300,40308],{},[1145,40301,40302],{},[1217,40303,40304,40306],{},[1156,40305,6797],{},[1919,40307,2780],{},[1172,40309,6802],{"encoding":1174}," není důkaz, že ",[1115,40312,40314],{"className":40313},[1136],[1138,40315,40316],{"xmlns":1140},[1142,40317,40318,40326],{},[1145,40319,40320],{},[1217,40321,40322,40324],{},[1156,40323,6797],{},[1919,40325,2780],{},[1172,40327,6802],{"encoding":1174}," platí."," U kabelů A\u002FB vyšlo ",[1115,40331,40333],{"className":40332},[1136],[1138,40334,40335],{"xmlns":1140},[1142,40336,40337,40345],{},[1145,40338,40339,40341,40343],{},[1156,40340,1110],{},[1148,40342,1914],{},[1919,40344,37713],{},[1172,40346,37716],{"encoding":1174},[1115,40348,40350],{"className":40349},[1136],[1138,40351,40352],{"xmlns":1140},[1142,40353,40354,40362],{},[1145,40355,40356],{},[1217,40357,40358,40360],{},[1156,40359,6797],{},[1919,40361,2780],{},[1172,40363,6802],{"encoding":1174}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1127,40366,40367,40370],{},[1445,40368,40369],{},"Před párovým nebo dvouvýběrovým t-testem ověřte normalitu."," U realitních odhadců vycházel párový t-test bez varování, ale Shapiro-Wilkův test na diferencích normalitu zamítl — správným testem byl párový Wilcoxonův test.",[1127,40372,40373,40380,40381,40384,40385,40387],{},[1445,40374,40375,34875,40377,40379],{},[1434,40376,37445],{},[1434,40378,32659],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[1434,40382,40383],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[1434,40386,37696],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1127,40389,40390,40393,40394,40397,40398,40415,40416,1247],{},[1445,40391,40392],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[1434,40395,40396],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,40399,40401],{"className":40400},[1136],[1138,40402,40403],{"xmlns":1140},[1142,40404,40405,40413],{},[1145,40406,40407],{},[1217,40408,40409,40411],{},[1156,40410,6797],{},[1919,40412,1921],{},[1172,40414,8200],{"encoding":1174}," v zadání, ne být ponechána na výchozí hodnotě ",[1434,40417,40418],{},"\"two.sided\"",[1127,40420,40421,40424,40425,40438],{},[1445,40422,40423],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,40426,40428],{"className":40427},[1136],[1138,40429,40430],{"xmlns":1140},[1142,40431,40432,40436],{},[1145,40433,40434],{},[1156,40435,6835],{},[1172,40437,6835],{"encoding":1174}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1437,40440,6607],{"id":6606},[1124,40442,40443,40448,40453,40458,40463,40468,40473],{},[1127,40444,40445],{},[6613,40446,6618],{"className":40447,"dataFsResolvedFilePath":6616,"href":6617},[1531],[1127,40449,40450],{},[6613,40451,11774],{"className":40452,"dataFsResolvedFilePath":6631,"href":6632},[1531],[1127,40454,40455],{},[6613,40456,11768],{"className":40457,"dataFsResolvedFilePath":6624,"href":6625},[1531],[1127,40459,40460],{},[6613,40461,11780],{"className":40462,"dataFsResolvedFilePath":6646,"href":6647},[1531],[1127,40464,40465],{},[6613,40466,6754],{"className":40467,"dataFsResolvedFilePath":6654,"href":6655},[1531],[1127,40469,40470],{},[6613,40471,1094],{"className":40472,"dataFsResolvedFilePath":11786,"href":11787},[1531],[1127,40474,40475],{},[6613,40476,6663],{"className":40477,"dataFsResolvedFilePath":6661,"href":6662},[1531],[1437,40479,6666],{"id":934},[1110,40481,6669,40482,6674],{},[6671,40483,6673],{},[6697,40485,40486],{},"html pre.shiki code .sP4rz, 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